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1
CHO, Y. M. "ANATOMY OF EINSTEIN'S THEORY: ABELIAN DECOMPOSITION OF GENERAL RELATIVITY." International Journal of Modern Physics: Conference Series 07 (January 2012): 116–47. http://dx.doi.org/10.1142/s2010194512004205.
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Treating Einstein's theory as a gauge theory of Lorentz group, we decompose the gravitational connection (the gauge potential of Lorentz group) Γμ into the restricted connection of the maximal Abelian subgroup of Lorentz group and the valence connection which transforms covariantly under Lorentz gauge transformation. With this decomposition we show that the Einstein's theory can be decomposed into the restricted part made of the restricted connection which has the full Lorentz gauge invariance and the valence part made of the valence connection which plays the role of gravitational source of the restricted gravity. We show that there are two different Abelian decomposition of Einstein's theory, the light-like (or null) decomposition and the non light-like (or non-null) decomposition. In this decomposition the role of the metric gμν is replaced by a four-index metric tensor gμν which transforms covariantly under the Lorentz group, and the metric-compatibility condition ∇αgμν = 0 of the connection is replaced by the gauge and generally covariant condition [Formula: see text]. The decomposition shows the existence of a restricted theory of gravitation which has the full general invariance but is much simpler and has less physical degrees of freedom than Einstein's theory. Moreover, it tells that the restricted gravity can be written as an Abelian gauge theory, which implies that the graviton can be described by a massless spin-one field.
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Shah, Mushtaq B., and Prince A. Ganai. "Quantum gauge freedom in the Lorentz violating background." International Journal of Geometric Methods in Modern Physics 15, no. 01 (2017): 1850009. http://dx.doi.org/10.1142/s0219887818500093.
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In this paper, we will study the Lorentz symmetry breaking down to its subgroup. A two-form gauge theory is investigated in the Lorentz violating background and it will be shown that this symmetry violation affects the structure of this gauge theory. In particular, we will study the gaugeon formalism and FFBRST for such a theory in this broken spacetime. In addition to Kugo-Ojima type condition, a thorough evaluation of quantum gauge freedom and gaugeon modes is carried out. We will explicitly demonstrate that in Lorentz broken spacetime, our reducible gauge theory fully depicts the physical aspects of gaugeon fields.
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El Hanafy, W., and G. G. L. Nashed. "Lorenz gauge fixing of f(T) teleparallel cosmology." International Journal of Modern Physics D 26, no. 14 (2017): 1750154. http://dx.doi.org/10.1142/s0218271817501541.
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In teleparallel gravity, we apply Lorenz type gauge fixing to cope with redundant degrees of freedom in the vierbein field. This condition is mainly to restore the Lorentz symmetry of the teleparallel torsion scalar. In cosmological application, this technique provides standard cosmology, turnaround, bounce or [Formula: see text]CDM as separate scenarios. We reconstruct the [Formula: see text] gravity which generates these models. We study the stability of the solutions by analyzing the corresponding phase portraits. Also, we investigate Lorenz gauge in the unimodular coordinates, it leads to unify a nonsingular bounce and Standard Model cosmology in a single model, where crossing the phantom divide line is achievable through a finite-time singularity of Type IV associated with a de Sitter fixed point. We reconstruct the unimodular [Formula: see text] gravity which generates the unified cosmic evolution showing the role of the torsion gravity to establish a healthy bounce scenario.
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GHOSH, SUBIR. "SPACETIME SYMMETRIES IN NONCOMMUTATIVE GAUGE THEORY: A HAMILTONIAN ANALYSIS." Modern Physics Letters A 19, no. 33 (2004): 2505–17. http://dx.doi.org/10.1142/s0217732304014963.
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We study spacetime symmetries in noncommutative (NC) gauge theory in the (constrained) Hamiltonian framework. The specific example of NC CP(1) model, posited in Ref. 9, has been considered. Subtle features of Lorentz invariance violation in NC field theory were pointed out in Ref. 13. Out of the two — observer and particle — distinct types of Lorentz transformations, symmetry under the former, (due to the translation invariance), is reflected in the conservation of energy and momentum in NC theory. The constant tensor θμν (the noncommutativity parameter) destroys invariance under the latter. In this paper we have constructed the Hamiltonian and momentum operators which are the generators of time and space translations respectively. This is related to the observer Lorentz invariance. We have also shown that the Schwinger condition and subsequently the Poincaré algebra is not obeyed and that one cannot derive a Lorentz covariant dynamical field equation. These features signal a loss of the Particle Lorentz symmetry. The basic observations in the present work will be relevant in the Hamiltonian study of a generic noncommutative field theory.
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Arbab, A. I., and M. Al-Ajmi. "The Modified Electromagnetism and the Emergent Longitudinal Wave." Applied Physics Research 10, no. 2 (2018): 45. http://dx.doi.org/10.5539/apr.v10n2p45.
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The classical theory of electromagnetism has been revisited and the possibility of longitudinal photon wave is explored. It is shown that the emergence of longitudinal wave is a consequence of Lorenz gauge (condition) violation. Proca, Vlaenderen & Waser and Arbab theories are investigated. The different approaches are compared to each other and the relevant equations are combined. The telegrapher’s equation can be obtained and with a specific choice of the function a Klein-Gordon equation of massive scalar field can be obtained. When the Lorentz gauge is violated by introducing the first order time derivative the emergence of the photon mass and the relevant longitudinal wave for the electromagnetic wave is apparnt.
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Chubykalo, Andrew E., and Roman Smirnov-Rueda. "Convection Displacement Current and Generalized Form of Maxwell–Lorentz Equations." Modern Physics Letters A 12, no. 01 (1997): 1–24. http://dx.doi.org/10.1142/s0217732397000029.
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Some mathematical inconsistencies in the conventional form of Maxwell's equations extended by Lorentz for a single charge system are discussed. To surmount these in the framework of Maxwellian theory, a novel convection displacement current is considered as additional and complementary to the famous Maxwell displacement current. It is shown that this form of the Maxwell–Lorentz equations is similar to that proposed by Hertz for electrodynamics of bodies in motion. Original Maxwell's equations can be considered as a valid approximation for a continuous and closed (or going to infinity) conduction current. It is also proved that our novel form of the Maxwell–Lorentz equations is relativistically invariant. In particular, a relativistically invariant gauge for quasistatic fields has been found to replace the non-invariant Coulomb gauge. The new gauge condition contains the famous relationship between electric and magnetic potentials for one uniformly moving charge that is usually attributed to the Lorentz transformations. Thus, for the first time, using the convection displacement current, a physical interpretation is given to the relationship between the components of the four-vector of quasistatic potentials. A rigorous application of the new gauge transformation with the Lorentz gauge transforms the basic field equations into a pair of differential equations responsible for longitudinal and transverse fields, respectively. The longitudinal components can be interpreted exclusively from the standpoint of the instantaneous "action at a distance" concept and leads to necessary conceptual revision of the conventional Faraday–Maxwell field. The concept of electrodynamics dualism is proposed for self-consistent classical electrodynamics. It implies simultaneous coexistence of instantaneous long-range (longitudinal) and Faraday–Maxwell short-range (transverse) interactions that resembles in this aspect the basic idea of Helmholtz's electrodynamics.
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SHABANOV, SERGEI V. "ABELIAN PROJECTION AND STUDIES OF GAUGE-VARIANT QUANTITIES IN THE LATTICE QCD WITHOUT GAUGE FIXING." Modern Physics Letters A 11, no. 13 (1996): 1081–93. http://dx.doi.org/10.1142/s0217732396001119.
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We suggest a new (dynamical) Abelian projection of the lattice QCD. It contains no gauge condition imposed on gauge fields so that Gribov copying is avoided. Configurations of gauge fields that turn into monopoles in the Abelian projection can be classified in a gauge-invariant way. In the continuum limit, the theory respects the Lorentz invariance. A similar dynamical reduction of the gauge symmetry is proposed for studies of gauge-variant correlators (like a gluon propagator) in the lattice QCD. Though the procedure is harder for numerical simulations, it is free of gauge-fixing artifacts, like the Gribov horizon and copies.
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TSEYTLIN, A. A. "LIGHT CONE SUPERSTRINGS IN ADS SPACE." International Journal of Modern Physics A 16, no. 05 (2001): 900–909. http://dx.doi.org/10.1142/s0217751x01003986.
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We discuss light-cone gauge description of type IIB Green-Schwarz superstring in AdS5× S5 with a hope to make progress towards understanding spectrum of this theory. As in flat space, fixing light-cone gauge consists of two steps: (i) fixing kappa symmetry in such a way that the fermionic part of the action does not depend on x-; (ii) fixing 2-d reparametrizations by x+=τ and a condition on 2-d metric. In curved AdS space the latter cannot be the standard conformal gauge and breaks manifest 2-d Lorentz invariance. It is natural, therefore, to work in phase-space framework, imposing the GGRT light-cone gauge conditions x+=τ, P+= const. We obtain the resulting light-cone superstring Hamiltonian.
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Liu, Chein-Shan. "The g-Based Jordan Algebra and Lie Algebra Formulations of the Maxwell Equations." Journal of Mechanics 20, no. 4 (2004): 285–96. http://dx.doi.org/10.1017/s1727719100003518.
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AbstractWhen it is usually using a bigger algebra system to formulate the Maxwell equations, in this paper we consider a real four-dimensional algebra to express the Maxwell equations without appealing to the imaginary number and higher dimensional algebras. In terms of g-based Jordan algebra formulation the Lorentz gauge condition is found to be a necessary and sufficient condition to render the second pair of Maxwell equations, while the first pair of Maxwell equations is proved to be an intrinsic algebraic property. Then, we transform the g-based Jordan algebra to a Lie algebra of the dilation proper orthochronous Lorentz group, which gives us an incentive to consider a linear matrix operator of the Lie type, rendering more easy to derive the Maxwell equations and the wave equations. The new formulations fully match the requirements for the classical electrodynamic equations and the Lorentz gauge condition. The mathematical advantage of our formulations is that they are irreducible in the sense that, when compared to the formulations which using other bigger algebras (e.g., biquaternions and Clifford algebras), the number of explicit components and operations is minimal. From this aspect, the g-based Jordan algebra and Lie algebra are the most suitable algebraic systems to implement the Maxwell equations into a more compact form.
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CASTELLANA, MICHELE, and GIOVANNI MONTANI. "BRST SYMMETRY TOWARDS THE GAUSS CONSTRAINT FOR GENERAL RELATIVITY." International Journal of Modern Physics A 23, no. 08 (2008): 1218–21. http://dx.doi.org/10.1142/s0217751x08040093.
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Quantization of systems with constraints can be carried on with several methods. In the Dirac's formulation the classical generators of gauge transformations are required to annihilate physical quantum states to ensure their gauge invariance. Carrying on BRST symmetry it is possible to get a condition on physical states which, differently from the Dirac's method, requires them to be invariant under the BRST transformation. Employing this method for the action of general relativity expressed in terms of the spin connection and tetrad fields with path integral methods, we construct the generator of BRST transformation associated with the underlying local Lorentz symmetry of the theory and write a physical state condition following from BRST invariance. The condition we gain differs form the one obtained within Ashtekar's canonical formulation, showing how we recover the latter only by a suitable choice of the gauge fixing functionals. We finally discuss how it should be possible to obtain all the requested physical state conditions associated with all the underlying gauge symmetries of the classical theory using our approach.
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Deeley, E. M. "A vector absorbing boundary condition for vector potential satisfying the Lorentz gauge." IEEE Transactions on Magnetics 32, no. 3 (1996): 858–61. http://dx.doi.org/10.1109/20.497376.
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MAJUMDAR, PARTHASARATHI. "COVARIANTLY QUANTIZED D=4, N=1 GREEN-SCHWARZ SIGMA MODELS." International Journal of Modern Physics A 06, no. 04 (1991): 599–611. http://dx.doi.org/10.1142/s0217751x91000356.
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The Batalin-Vilkovisky quantization technique is used to provide a manifestly Lorentz covariant quantization of the σ-model describing the D=4 heterotic Green-Schwarz superstring propagating in a background superpsace consisting of minimal supergravity “entangled” with a tensor multiplet. The ultraviolet finiteness properties of the one-loop effective action are shown to be identical to those obtained earlier using a manifestly non-covariant gauge-fixing condition.
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Maggiore, Nicola. "From Chern–Simons to Tomonaga–Luttinger." International Journal of Modern Physics A 33, no. 02 (2018): 1850013. http://dx.doi.org/10.1142/s0217751x18500136.
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A single-sided boundary is introduced in the three-dimensional Chern–Simons model. It is shown that only one boundary condition for the gauge fields is possible, which plays the twofold role of chirality condition and bosonization rule for the two-dimensional Weyl fermion describing the degrees of freedom of the edge states of the Fractional Quantum Hall Effect. The symmetry on the boundary is derived, which determines the effective two-dimensional action, whose equation of motion coincides with the continuity equation of the Tomonaga–Luttinger theory. The role of Lorentz symmetry and of discrete symmetries on the boundary is also discussed.
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Yoshida, Norinobu. "Unified treatment of scalar and vector potential fields with lorentz gauge condition by spatial network expression (invited article)." International Journal of Microwave and Millimeter-Wave Computer-Aided Engineering 3, no. 3 (1993): 165–74. http://dx.doi.org/10.1002/mmce.4570030304.
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Dautbasic, Nedis, and Adnan Mujezinovic. "Time domain solution of electromagnetic radiation model of the grounding system excited by pulse current." Nuclear Technology and Radiation Protection 35, no. 1 (2020): 74–81. http://dx.doi.org/10.2298/ntrp2001074d.
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This paper deals with an advanced electromagnetic radiation approach for analyzing the time-domain performance of grounding systems under pulse excitation currents. The model of the grounding systems presented within this paper is based on the homogeneous Pocklington integro-differential equation for the calculation of the current distribution on the grounding system and Lorentz gauge condition which is used for the grounding system transient voltage calculation. For the solution of the Pocklington integro-differential equation, the indirect boundary element method and marching on-in time method are used. Fur- thermore, the solution technique for the calculation of the grounding system transient voltage is presented. The numerical model for the calculation of the grounding system transients was verified by comparing it with onsite measurement results.
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Chanyal, B. C. "A new development in quantum field equations of dyons." Canadian Journal of Physics 96, no. 11 (2018): 1192–200. http://dx.doi.org/10.1139/cjp-2017-0996.
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In this study, we describe a novel approach to quantum phenomena of the generalized electromagnetic fields of dyons with quaternionic analysis. Starting with quaternionic quantum wave equations, we have established a quantized condition for time coordinate that transforms microscopic to macroscopic fields. In view of the classical electromagnetic field equations, we propose a new set of quantized Proca–Maxwell’s equations for dyons. Furthermore, a quantized form of four-current densities and the quantized Lorentz gauge conditions for electric and magnetic potentials, respectively, of dyons are obtained. We have established the new quantized continuity equations for electric and magnetic densities of dyons, which are associated with a torque density result from the two spin states. The quantized Klein–Gordon-like field equations and the unified quaternionic electromagnetic potential wave equations for massive dyons are demonstrated. Moreover, we investigate the quaternionic quantized relativistic Dirac field equations for massive dyons, which indicate that the antiparticle of dyons will exist, called antidyons.
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Semenov-Tyan-Shanskii, M. A., and V. A. Franke. "A variational principle for the Lorentz condition and restriction of the domain of path integration in non-abelian gauge theory." Journal of Soviet Mathematics 34, no. 5 (1986): 1999–2004. http://dx.doi.org/10.1007/bf01095108.
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Bellorín, Jorge, and Alvaro Restuccia. "Einstein’s quadrupole formula from the kinetic-conformal Hořava theory." International Journal of Modern Physics D 27, no. 01 (2017): 1750174. http://dx.doi.org/10.1142/s0218271817501747.
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We analyze the radiative and nonradiative linearized variables in a gravity theory within the family of the nonprojectable Hořava theories, the Hořava theory at the kinetic-conformal point. There is no extra mode in this formulation, the theory shares the same number of degrees of freedom with general relativity. The large-distance effective action, which is the one we consider, can be given in a generally-covariant form under asymptotically flat boundary conditions, the Einstein-aether theory under the condition of hypersurface orthogonality on the aether vector. In the linearized theory, we find that only the transverse-traceless tensorial modes obey a sourced wave equation, as in general relativity. The rest of variables are nonradiative. The result is gauge-independent at the level of the linearized theory. For the case of a weak source, we find that the leading mode in the far zone is exactly Einstein’s quadrupole formula of general relativity, if some coupling constants are properly identified. There are no monopoles nor dipoles in this formulation, in distinction to the nonprojectable Horava theory outside the kinetic-conformal point. We also discuss some constraints on the theory arising from the observational bounds on Lorentz-violating theories.
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Edwards, J. P., and M. Kirchbach. "Massless Rarita–Schwinger field from a divergenceless antisymmetric tensor-spinor of pure spin-3/2." International Journal of Modern Physics A 34, no. 11 (2019): 1950060. http://dx.doi.org/10.1142/s0217751x1950060x.
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We construct the Rarita–Schwinger basis vectors, [Formula: see text], spanning the direct product space, [Formula: see text], of a massless four-vector, [Formula: see text], with massless Majorana spinors, [Formula: see text], together with the associated field-strength tensor, [Formula: see text]. The [Formula: see text] space is reducible and contains one massless subspace of a pure spin-[Formula: see text]. We show how to single out the latter in a unique way by acting on [Formula: see text] with an earlier derived momentum independent projector, [Formula: see text], properly constructed from one of the Casimir operators of the algebra [Formula: see text] of the homogeneous Lorentz group. In this way, it becomes possible to describe the irreducible massless [Formula: see text] carrier space by means of the antisymmetric tensor of second rank with Majorana spinor components, defined as [Formula: see text]. The conclusion is that the [Formula: see text] bi-vector spinor field can play the same role with respect to a [Formula: see text] gauge field as the bi-vector, [Formula: see text], associated with the electromagnetic field-strength tensor, [Formula: see text], plays for the Maxwell gauge field, [Formula: see text]. Correspondingly, we find the free electromagnetic field equation, [Formula: see text], is paralleled by the free massless Rarita–Schwinger field equation, [Formula: see text], supplemented by the additional condition, [Formula: see text], a constraint that invokes the Majorana sector.
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Pastor, Ignacio, Ramón F. Álvarez-Estrada, Luis Roso, and Francisco Castejón. "Fundamental Studies on Electron Dynamics in Exact Paraxial Beams with Angular Momentum." Photonics 9, no. 10 (2022): 693. http://dx.doi.org/10.3390/photonics9100693.
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Classical electromagnetic radiation with orbital angular momentum (OAM), described by nonvanishing vector and scalar potentials (namely, Lorentz gauge) and under Lorentz condition, is considered. They are employed to describe paraxial laser beams, thereby including non-vanishing longitudinal components of electric and magnetic fields. The relevance of the latter on electron dynamics is investigated in the reported numerical experiments. The lowest corrections to the paraxial approximation appear to have a negligeable influence in the regimes treated here. Incoherent Thomson scattering (TS) from a sample of free electrons moving subject to the paraxial fields is studied and investigated as a beam diagnosis tool. Numerical computations elucidate the nature and conditions for the so called trapped solutions (electron motions bounded in the transverse plane of the laser and drifting along the propagation direction) in long quasi-steady laser beams. The influence of laser parameters, in particular, the laser beam size and the non-vanishing longitudinal field components, essential for the paraxial approximation to hold, are studied. When the initial conditions of the electrons are sufficiently close to the origin, a simplified model Hamiltonian to the full relativistic one is introduced. It yields results comparing quite well quantitatively with the observed amplitudes, phase relationships and frequencies of oscillation of trapped solutions (at least for wide laser beam sizes). Genuine pulsed paraxial fields with OAM and their features, modeling true ultra-short pulses are also studied for two cases, one of wide laser beam spot (100 μm) and other with narrow beam size of 6.4 μm. To this regard, the asymptotic distribution of the kinetic energy of the electrons as a function of their initial position over the transverse section is analyzed. The relative importance of the transverse structure effects and the role of longitudinal fields is addressed. By including the full paraxial fields, the asymptotic distribution of kinetic energy of an electron population distributed across the laser beam section, has a nontrivial and unexpected rotational symmetry along the optical propagation axis.
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Monakhov, Vadim. "Vacuum and Spacetime Signature in the Theory of Superalgebraic Spinors." Universe 5, no. 7 (2019): 162. http://dx.doi.org/10.3390/universe5070162.
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A new formalism involving spinors in theories of spacetime and vacuum is presented. It is based on a superalgebraic formulation of the theory of algebraic spinors. New algebraic structures playing role of Dirac matrices are constructed on the basis of Grassmann variables, which we call gamma operators. Various field theory constructions are defined with use of these structures. We derive formulas for the vacuum state vector. Five operator analogs of five Dirac gamma matrices exist in the superalgebraic approach as well as two additional operator analogs of gamma matrices, which are absent in the theory of Dirac spinors. We prove that there is a relationship between gamma operators and the most important physical operators of the second quantization method: number of particles, energy–momentum and electric charge operators. In addition to them, a series of similar operators are constructed from the creation and annihilation operators, which are Lorentz-invariant analogs of Dirac matrices. However, their physical meaning is not yet clear. We prove that the condition for the existence of spinor vacuum imposes restrictions on possible variants of the signature of the four-dimensional spacetime. It can only be (1, − 1 , − 1 , − 1 ), and there are two additional axes corresponding to the inner space of the spinor, with a signature ( − 1 , − 1 ). Developed mathematical formalism allows one to obtain the second quantization operators in a natural way. Gauge transformations arise due to existence of internal degrees of freedom of superalgebraic spinors. These degrees of freedom lead to existence of nontrivial affine connections. Proposed approach opens perspectives for constructing a theory in which the properties of spacetime have the same algebraic nature as the momentum, electromagnetic field and other quantum fields.
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Escobar, C. A., and L. F. Urrutia. "Extended Nambu models: Their relation to gauge theories." International Journal of Modern Physics A 32, no. 14 (2017): 1750077. http://dx.doi.org/10.1142/s0217751x17500774.
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Yang–Mills theories supplemented by an additional coordinate constraint, which is solved and substituted in the original Lagrangian, provide examples of the so-called Nambu models, in the case where such constraints arise from spontaneous Lorentz symmetry breaking. Some explicit calculations have shown that, after additional conditions are imposed, Nambu models are capable of reproducing the original gauge theories, thus making Lorentz violation unobservable and allowing the interpretation of the corresponding massless gauge bosons as the Goldstone bosons arising from the spontaneous symmetry breaking. A natural question posed by this approach in the realm of gauge theories is to determine under which conditions the recovery of an arbitrary gauge theory from the corresponding Nambu model, defined by a general constraint over the coordinates, becomes possible. We refer to these theories as extended Nambu models (ENM) and emphasize the fact that the defining coordinate constraint is not treated as a standard gauge fixing term. At this level, the mechanism for generating the constraint is irrelevant and the case of spontaneous Lorentz symmetry breaking is taken only as a motivation, which naturally bring this problem under consideration. Using a nonperturbative Hamiltonian analysis we prove that the ENM yields the original gauge theory after we demand current conservation for all time, together with the imposition of the Gauss laws constraints as initial conditions upon the dynamics of the ENM. The Nambu models yielding electrodynamics, Yang–Mills theories and linearized gravity are particular examples of our general approach.
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ESPOSITO, GIAMPIERO, ALEXANDER YU. KAMENSHCHIK, and KLAUS KIRSTEN. "ZERO-POINT ENERGY OF A CONDUCTING SPHERICAL SHELL." International Journal of Modern Physics A 14, no. 02 (1999): 281–300. http://dx.doi.org/10.1142/s0217751x99000154.
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The zero-point energy of a conducting spherical shell is evaluated by imposing boundary conditions on the potential Aμ, and on the ghost fields. The scheme requires that temporal and tangential components of Aμ perturbations should vanish at the boundary, jointly with the gauge-averaging functional, first chosen to be of the Lorentz type. Gauge invariance of such boundary conditions is then obtained provided that the ghost fields vanish at the boundary. Normal and longitudinal modes of the potential obey an entangled system of eigenvalue equations, whose solution is a linear combination of Bessel functions under the above assumptions, and with the help of the Feynman choice for a dimensionless gauge parameter. Interestingly, ghost modes cancel exactly the contribution to the Casimir energy resulting from transverse and temporal modes of Aμ, jointly with the decoupled normal mode of Aμ. Moreover, normal and longitudinal components of Aμ for the interior and the exterior problem give a result in complete agreement with the one first found by Boyer, who studied instead boundary conditions involving TE and TM modes of the electromagnetic field. The coupled eigenvalue equations for perturbative modes of the potential are also analyzed in the axial gauge, and for arbitrary values of the gauge parameter. The set of modes which contribute to the Casimir energy is then drastically changed, and comparison with the case of a flat boundary sheds some light on the key features of the Casimir energy in noncovariant gauges.
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Seifert, Michael. "Lorentz-Violating Gravity Models and the Linearized Limit." Symmetry 10, no. 10 (2018): 490. http://dx.doi.org/10.3390/sym10100490.
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Many models in which Lorentz symmetry is spontaneously broken in a curved spacetime do so via a “Lorentz-violating” (LV) vector or tensor field, which dynamically takes on a vacuum expectation value and provides additional local geometric structure beyond the metric. The kinetic terms of such a field will not necessarily be decoupled from the kinetic terms of the metric, and will generically lead to a set of coupled equations for the perturbations of the metric and the LV field. In some models, however, the imposition of certain additional conditions can decouple these equations, yielding an “effective equation” for the metric perturbations alone. The resulting effective equation may depend on the metric in a gauge-invariant way, or it may be gauge-dependent. The only two known models yielding gauge-invariant effective equations involve differential forms; I show in this work that the obvious generalizations of these models do not yield gauge-invariant effective equations. Meanwhile, I show that a gauge-dependent effective equation may be obtained from any “tensor Klein–Gordon” model under similar assumptions. Finally, I discuss the implications of this work in the search for Lorentz-violating gravitational effects.
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Joshi, I., and J. S. Garia. "Electromagnetic Wave Equations of Dyon in Arbitrary Media." Journal of Scientific Research 12, no. 2 (2020): 161–67. http://dx.doi.org/10.3329/jsr.v12i2.43635.
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Dyon is a hypothetical particle in high energy physics that carries simultaneously both electric and magnetic charge. A dyon with zero electric charge is referred to a magnetic monopole. The paper, reports a simple reformulation of Maxwell equations for dyon in arbitrary media. The Lorentz, Coulomb gauge conditions and the wave equations of dyon in arbitrary media are derived in a simple and compact manner.
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Jeong-Sik Choi, Duk-In Choi, and Soon-Chul Yang. "Generalized Lorentz Gauge and Boundary Conditions in Partially Dielectric-Loaded Cylindrical Waveguide (Short Paper)." IEEE Transactions on Microwave Theory and Techniques 35, no. 11 (1987): 1065–66. http://dx.doi.org/10.1109/tmtt.1987.1133808.
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Soni, S. K., and Simmi Singh. "Feynman's Proof of the Lorentz Force Equations with Dissipation Linear in the Velocity." Modern Physics Letters A 12, no. 33 (1997): 2523–33. http://dx.doi.org/10.1142/s021773239700265x.
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We present the Feynman proof of the Lorentz force law plus dissipative terms with a linear dependence on the velocity vector. In addition, we discuss in this context the inverse problem of the calculus of variations and the inverse problem for the Poisson dynamics. Given the equations of motion, the Helmholtz conditions for the inverse problem of the calculus of variations are solved and the Lagrangian is shown to have the nonsingular gauge type form.
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Dai, Jialiang. "A canonical Hamiltonian analysis of Podolsky’s generalized electrodynamics in first-order formalism." International Journal of Modern Physics A 36, no. 10 (2021): 2150068. http://dx.doi.org/10.1142/s0217751x21500688.
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We give a canonical Hamiltonian analysis of Podolsky’s generalized electrodynamics by introducing two sets of new variables which help us transform the Lagrangian into an equivalent first-order formalism. After eliminating the unphysical sector, we calculate the physical degrees of freedom of the higher derivative system and obtain the Dirac brackets in the reduced phase space. Then with the aid of the first-class constraints, we construct the independent gauge generator which is closely connected with the BRST charge and the BRST-invariant Hamiltonian. Finally, by choosing appropriate gauge-fixing fermion, we evaluate the path integral of this higher derivative constrained system in BRST quantization scheme with the generalized Lorenz gauge condition.
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HATSUDA, MACHIKO. "BRST FIELD THEORIES FOR A QUANTUM LORENTZ PARTICLE." International Journal of Modern Physics A 07, no. 06 (1992): 1187–213. http://dx.doi.org/10.1142/s0217751x9200051x.
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From the study of string field theory, first quantized BRST symmetry is known to be a guiding principle in constructing field theories. We construct the first quantized BRST charge QB for a quantum Lorentz particle which is characterized by the constraints which are expressed in terms of (inhomogeneous) Lorentz generators. It is shown that the BRST cohomology of this system includes only the field strengths and not the fundamental gauge fields with nontrivial norms. By using this BRST charge, we obtain the field theory Lagrangian via the ∫ΨQBΨ construction, which leads to field equations for fields with arbitrary spin. However, this action cannot be used to derive a second quantized theory except for Dirac fields. For antisymmetric tensor fields, we can get the correct second quantized theories if we introduce extra conditions.
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Bufalo, R., B. M. Pimentel, and D. E. Soto. "Normalizability analysis of the generalized quantum electrodynamics from the causal point of view." International Journal of Modern Physics A 32, no. 27 (2017): 1750165. http://dx.doi.org/10.1142/s0217751x17501652.
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The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the inductive method order-by-order and, of course, it depends on the particular physical model. In this work we shall study the normalizability of the generalized quantum electrodynamics in the framework of the causal approach. Furthermore, we analyze the implication of the gauge invariance onto the model and obtain the respective Ward–Takahashi–Fradkin identities.
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Belich, H., M. A. Santos, and M. T. D. Orlando. "The gauge sector of the SME with Lorentz-symmetry violation by symplectic projector method." Modern Physics Letters A 30, no. 35 (2015): 1550191. http://dx.doi.org/10.1142/s0217732315501916.
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We propose to analyze a modified electromagnetism inspired from the gauge sector of the Standard Model extension (SME). From the point of view of a canonical formulation, we carried out the usual analysis on the constraints structure of the odd sector (Carroll–Field–Jackiw term) and a Maxwell term with an effective metric. This effective metric is obtained by a vectorial decomposition of the CPT-even term, that is absorbed in the ordinary Maxwell term. Using symplectic projector method (SPM), we obtain the dispersions relations and we have verified conditions of stability to determine the valid spectrum.
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Diaz, Henry, O. Pereyra Ravinez, and C. Lopez Lozano. "Mass Generation of the Scalars Bosons in a Left-Right Symmetric Model with two Bidoublets." Journal of Physics: Conference Series 2678, no. 1 (2023): 012007. http://dx.doi.org/10.1088/1742-6596/2678/1/012007.
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Abstract The search for new Physics justified by new discoverys, motivate among others, the realization of new models called Extensions of the Standard Model (ESM) which must include at low energy the Standar Model. (SM) The electroweak symmetry group SU(2) L ⊗ U(1) Y to the gauge group with left-right symmetry SU(2) L ⊗ SU(2) R ⊗ U(1) B − L ⊗ 𝒫, represents one of the minimal extensions of the SM, in which 𝒫 is a parity discrete symmetry such that left-right coupling constants satisfied gL = gR , and according to the hierarchy in the symmetry breaking (conditions that must be met by the vacuum expectation values introduced in the model) allow to obtain the SM. The aim of this work is to identify the Higgs boson of the SM, considering a more general scalar potential that must respect all the symmetries (local gauge invariant, discrete symmetries and Lorentz invariant) established in the model. We will take into account those previous works about the hierarchy conditions and certain approximations that must satisfy the vacuum expectation values for obtain greater simplicity in the caculations of scalar masses of the model.
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Roth, Thomas E., and Colin A. Braun. "Theoretical and Numerical Study of Wave Port Boundary Conditions for Lorenz Gauge Potential-based Finite Element Methods." Progress In Electromagnetics Research C 131 (2023): 119–33. http://dx.doi.org/10.2528/pierc23010607.
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Chen, Qingrui, Shuqing Ma, Lilun Zhang, Shikun Dai, and Jiaxuan Ling. "Three-dimensional modeling of Marine Controlled Source Electromagnetic field using a space-wavenumber domain method." Journal of Physics: Conference Series 2718, no. 1 (2024): 012055. http://dx.doi.org/10.1088/1742-6596/2718/1/012055.
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Abstract Under complex conditions, the three-dimensional modeling of Marine Controlled Source Electromagnetic field requires a significant amount of computation, resulting in slow calculation speed and high storage requirements. To solve these problems, we propose a 3D numerical simulation method of electromagnetic field in the space-wavenumber domain under the Lorenz gauge. Firstly, the new method utilizes the two-dimensional Fourier transform in the horizontal direction to transform the 3D partial differential equations of the Lorenz vector potentials into multiple independent ordinary differential equations. Secondly, the finite element method is used to solve the ordinary differential equations. The fields in the spatial domain are then obtained by using the inverse Fourier transform, and finally, an iterative method with a compact operator is applied to approximate the true solution. The approach requires less computation and storage, and the algorithm is highly parallel, which effectively improves the efficiency of 3D forward modeling of electromagnetic fields. The correctness, effectiveness, and computational efficiency of the method are verified by the design model.
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Chanyal, B. C. "A relativistic quantum theory of dyons wave propagation." Canadian Journal of Physics 95, no. 12 (2017): 1200–1207. http://dx.doi.org/10.1139/cjp-2017-0080.
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Beginning with the quaternionic generalization of the quantum wave equation, we construct a simple model of relativistic quantum electrodynamics for massive dyons. A new quaternionic form of unified relativistic wave equation consisting of vector and scalar functions is obtained, and also satisfy the quaternionic momentum eigenvalue equation. Keeping in mind the importance of quantum field theory, we investigate the relativistic quantum structure of electromagnetic wave propagation of dyons. The present quantum theory of electromagnetism leads to generalized Lorentz gauge conditions for the electric and magnetic charge of dyons. We also demonstrate the universal quantum wave equations for two four-potentials as well as two four-currents of dyons. The generalized continuity equations for massive dyons in case of quantum fields are expressed. Furthermore, we concluded that the quantum generalization of electromagnetic field equations of dyons can be related to analogous London field equations (i.e., current to electromagnetic fields in and around a superconductor).
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Lubicz, Vittorio, Lorenzo Riggio, Giorgio Salerno, Silvano Simula та Cecilia Tarantino. "D → π and D → K semileptonic form factors with Nf = 2 + 1 + 1 twisted mass fermions". EPJ Web of Conferences 175 (2018): 13026. http://dx.doi.org/10.1051/epjconf/201817513026.
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We present a lattice determination of the vector and scalar form factors of the D → π(K)lv semileptonic decays, which are relevant for the extraction of the CKM matrix elements |Vcd| and |Vcs| from experimental data. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 +1 flavors of dynamical quarks. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV. The matrix elements of both vector and scalar currents are determined for a plenty of kinematical conditions in which parent and child mesons are either moving or at rest. Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data and included in the decomposition of the current matrix elements in terms of additional form factors. After the extrapolations to the physical pion mass and to the continuum limit the vector and scalar form factors are determined in the whole kinematical region from q2 = 0 up to [see formula in PDF] accessible in the experiments, obtaining a good overall agreement with experiments, except in the region at high values of q2 where some deviations are visible.
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Alba, David, Horace W. Crater, and Luca Lusanna. "Towards relativistic atomic physics. Part II. Collective and relative relativistic variables for a system of charged articles plus the electromagnetic field." Canadian Journal of Physics 88, no. 6 (2010): 425–63. http://dx.doi.org/10.1139/p09-038.
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In this second paper, we complete the classical description of an isolated system of “charged positive-energy particles, with Grassmann-valued electric charges and mutual Coulomb interaction, plus a transverse electromagnetic field” in the rest-frame instant form of dynamics. In particular, we show how to determine a collective variable associated with the internal 3-center of mass on the instantaneous 3-spaces, to be eliminated with the constraints [Formula: see text]. Here, [Formula: see text] is the Lorentz boost generator in the unfaithful internal realization of the Poincaré group and its vanishing is the gauge-fixing to the rest-frame conditions [Formula: see text]. We show how to find this collective variable for the following isolated systems: (a) charged particles with a Coulomb plus Darwin mutual interaction; (b) transverse radiation field; (c) charged particles with a mutual Coulomb interaction plus a transverse electro-magnetic field. Then we define the Dixon multipolar expansion for the open particle subsystem. We also define the relativistic electric dipole approximation of atomic physics in the rest-frame instant form and we find a possible relativistic generalization of the electric dipole representation.
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Lubicz, Vittorio, Lorenzo Riggio, Giorgio Salerno, Silvano Simula та Cecilia Tarantino. "Tensor form factor for the D → π(K) transitions with Twisted Mass fermions." EPJ Web of Conferences 175 (2018): 13022. http://dx.doi.org/10.1051/epjconf/201817513022.
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We present a preliminary lattice calculation of the D → π and D → K tensor form factors fT (q2) as a function of the squared 4-momentum transfer q2. ETMC recently computed the vector and scalar form factors f+(q2) and f0(q2) describing D → π(K)lv semileptonic decays analyzing the vector current and the scalar density. The study of the weak tensor current, which is directly related to the tensor form factor, completes the set of hadronic matrix element regulating the transition between these two pseudoscalar mesons within and beyond the Standard Model where a non-zero tensor coupling is possible. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 flavors of dynamical quarks. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV and with the valence heavy quark in the mass range from ≃ 0.7 mc to ≃ 1.2mc. The matrix element of the tensor current are determined for a plethora of kinematical conditions in which parent and child mesons are either moving or at rest. As for the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data. We will present preliminary results on the removal of such hypercubic lattice effects.
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Dahm, R. "On the Photon Vertex and Half-Integer Spin." Journal of Physics: Conference Series 2667, no. 1 (2023): 012006. http://dx.doi.org/10.1088/1742-6596/2667/1/012006.
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Abstract When rewriting the photon vertex of quantum electrodynamics in terms of geometrical quantities, various elements can be mapped directly to objects and properties known from classical projective geometry (PG). Elements of P 5 when mapped to line reps in P 3 exhibit their intrinsic Lorentz invariance associated to automorphisms of the Plücker-Klein quadric M 4 2 , and line reps when expressed by point or plane coordinates introduce (one-parameter) pencils, or formally gl(2,ℝ), or gl(1,ℍ) which covers su(2)⊕u(1). This introduces binary forms and, using a potential approach of central forces, Schrödinger or Laplace equations and the respective special functions, as well as the projective generation of quadrics like in Dirac’s approach which legitimates Clifford algebra elements as linear factors in invariant theory and the quadratic algebra to represent geometry. Physically, this identification allows for the classical concept of moments in terms of tetrahedrons which on the one hand relates to previous work on SU(4) and SU*(4) in quantum representations. On the other hand, it relates to the classical physical definitions, however, exhibiting a factor 2 between contemporary (euclidean) moments and the tetrahedral construction used in the vertex. Finally, we discuss the equilibrium conditions with respect to gauge and Yang-Mills theories in general as well as the related objects and their transformation theory.
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Radyushkin, A. V. "Theory and applications of parton pseudodistributions." International Journal of Modern Physics A 35, no. 05 (2020): 2030002. http://dx.doi.org/10.1142/s0217751x20300021.
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We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator [Formula: see text] of the parton fields is a function [Formula: see text] of Lorentz invariants [Formula: see text], the Ioffe time, and the invariant interval [Formula: see text]. This observation allows to extract the Ioffe-time distribution [Formula: see text] from Euclidean separations [Formula: see text] accessible on the lattice. Another basic feature is the use of the ratio [Formula: see text], that allows to eliminate artificial ultraviolet divergence generated by the gauge link for spacelike intervals. The remaining [Formula: see text]-dependence of the reduced Ioffe-time distribution [Formula: see text] corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions [Formula: see text] using matching relations. The [Formula: see text]-dependence of [Formula: see text] governs the [Formula: see text]-dependence of parton densities [Formula: see text]. The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now in progress.
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Mavromatos, Nick E. "Anomalies, the Dark Universe and Matter-Antimatter asymmetry." Journal of Physics: Conference Series 2533, no. 1 (2023): 012017. http://dx.doi.org/10.1088/1742-6596/2533/1/012017.
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Abstract I review a (3+1)-dimensional, string-inspired cosmological model with gravitational anomalies (of Chern-Simons (CS) type) at early epochs, and a totally-antisymmetric torsion, dual to a massless axion-like field (“gravitational axion”), which couples to the CS term. Under appropriate conditions, primordial gravitational waves can condense, leading to a condensate of the CS anomaly term. As a consequence, one obtains inflation in this theory, of running-vacuum-model (RVM) type, without the need for external inflatons. At the end of the inflationary era, chiral fermionic matter is generated, whose gravitational anomalies cancel the primordial ones. On the other hand, chiral anomalies of gauge type, which are also generated by the chiral matter, remain present during the post-inflationary epochs and become responsible for the generation of a non-perturbative mass for the torsion-related gravitational axion, which, in this way, might play the rôle of a Dark Matter component of geometrical origin. Moreover, in this model, stringy non-perturbative effects during the RVM inflationary phase generate periodic structures for the potential of axion-like particles that arise due to compactification, and co-exist with the gravitational axions. Such periodic potential modulations may lead to an enhanced production of primordial black holes during inflation, which in turn affects the profile of the generated gravitational waves during the radiation era, with potentially observable consequences. This model also entails an unconventional mechanism for Leptogenesis, due to Lorentz-violating backgrounds of the gravitational axions that are generated during inflation, as a consequence of the anomaly condensates, and remain undiluted in the radiation era.
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Zhang, Yang, and Xuan Ye. "Regularized Stress Tensor of Vector Fields in de Sitter Space." Universe 11, no. 2 (2025): 72. https://doi.org/10.3390/universe11020072.
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We study the Stueckelberg field in de Sitter space, which is a massive vector field with the gauge fixing (GF) term 12ζ(Aμ;μ)2. We obtain the vacuum stress tensor, which consists of the transverse, longitudinal, temporal, and GF parts, and each contains various UV divergences. By the minimal subtraction rule, we regularize each part of the stress tensor to its pertinent adiabatic order. The transverse stress tensor is regularized to the 0th adiabatic order, while the longitudinal, temporal, and GF stress tensors are regularized to the 2nd adiabatic order. The resulting total regularized vacuum stress tensor is convergent and maximally symmetric, has a positive energy density, and respects the covariant conservation, and thus, it can be identified as the cosmological constant that drives the de Sitter inflation. Under the Lorenz condition Aμ;μ=0, the regularized Stueckelberg stress tensor reduces to the regularized Proca stress tensor that contains only the transverse and longitudinal modes. In the massless limit, the regularized Stueckelberg stress tensor becomes zero, and is the same as that of the Maxwell field with the GF term, and no trace anomaly exists. If the order of adiabatic regularization were lower than our prescription, some divergences would remain. If the order were higher, say, under the conventional 4th-order regularization, more terms than necessary would be subtracted off, leading to an unphysical negative energy density and the trace anomaly simultaneously.
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Shenoy, Vighnesh, Prathvi Shenoy, and Santhosh Krishnan Venkata. "Accurate Liquid Level Measurement with Minimal Error: A Chaotic Observer Approach." Computation 12, no. 2 (2024): 29. http://dx.doi.org/10.3390/computation12020029.
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This paper delves into precisely measuring liquid levels using a specific methodology with diverse real-world applications such as process optimization, quality control, fault detection and diagnosis, etc. It demonstrates the process of liquid level measurement by employing a chaotic observer, which senses multiple variables within a system. A three-dimensional computational fluid dynamics (CFD) model is meticulously created using ANSYS to explore the laminar flow characteristics of liquids comprehensively. The methodology integrates the system identification technique to formulate a third-order state–space model that characterizes the system. Based on this mathematical model, we develop estimators inspired by Lorenz and Rossler’s principles to gauge the liquid level under specified liquid temperature, density, inlet velocity, and sensor placement conditions. The estimated results are compared with those of an artificial neural network (ANN) model. These ANN models learn and adapt to the patterns and features in data and catch non-linear relationships between input and output variables. The accuracy and error minimization of the developed model are confirmed through a thorough validation process. Experimental setups are employed to ensure the reliability and precision of the estimation results, thereby underscoring the robustness of our liquid-level measurement methodology. In summary, this study helps to estimate unmeasured states using the available measurements, which is essential for understanding and controlling the behavior of a system. It helps improve the performance and robustness of control systems, enhance fault detection capabilities, and contribute to dynamic systems’ overall efficiency and reliability.
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Alba, David, Horace W. Crater, and Luca Lusanna. "Towards relativistic atomic physics. Part 1. The rest-frame instant form of dynamics and a canonical transformation for a system of charged particles plus the electro-magnetic field." Canadian Journal of Physics 88, no. 6 (2010): 379–424. http://dx.doi.org/10.1139/p09-037.
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A complete exposition of the rest-frame instant form of dynamics for arbitrary isolated systems (particles, fields, strings, fluids) admitting a Lagrangian description is given. The starting point is the parametrized Minkowski theory describing the system in arbitrary admissible noninertial frames in Minkowski space-time, which allows one to define the energy-momentum tensor of the system and to show the independence of the description from the clock synchronization convention and from the choice of the 3-coordinates. The restriction to the inertial rest frame, centered on the inertial observer having the Fokker–Pryce center-of-inertia world line, and the study of relativistic collective variables replacing the nonrelativistic center of mass lead to the description of the isolated system as a decoupled globally defined noncovariant canonical external center of mass carrying a pole–dipole structure (the invariant mass M and the rest spin [Formula: see text] of the system) and an external realization of the Poincaré group. Mc and [Formula: see text] are the energy and angular momentum of a unfaithful internal realization of the Poincaré group built with the energy-momentum tensor of the system and acting inside the instantaneous Wigner 3-spaces where all the 3-vectors are Wigner covariant. The vanishing of the internal 3-momentum and of the internal Lorentz boosts eliminate the internal 3-center of mass inside the Wigner 3-spaces, so that at the end the isolated system is described only by Wigner-covariant canonical internal relative variables. Then an isolated system of positive-energy-charged scalar articles with mutual Coulomb interaction plus a transverse electromagnetic field in the radiation gauge is investigated as a classical background for defining relativistic atomic physics. The electric charges of the particles are Grassmann-valued to regularize the self-energies. The external and internal realizations of the Poincaré algebra in the rest-frame instant form of dynamics are found. This allows one to define explicitly the rest-frame conditions and their gauge-fixings (needed for the elimination of the internal 3-center of mass) for this isolated system. It is shown that there is a canonical transformation that allows one to describe the isolated system as a set of Coulomb-dressed charged particles interacting through a Coulomb plus Darwin potential plus a free transverse radiation field: these two subsystems are not mutually interacting (the internal Poincaré generators are a direct sum of the two components) and are interconnected only by the rest-frame conditions and the elimination of the internal 3-center of mass. Therefore in this framework with a fixed number of particles there is a way out from the Haag theorem, at least at the classical level.
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Miyashita, Tomofumi. "(Digital Presentation) Additional Voltage Loss in Terms of Electromagnetic Potential Related to Jarzynski’s Equality Using Sm-Doped Ceria Electrolytes in Wagner’s Equation for SOFCs." ECS Meeting Abstracts MA2022-01, no. 41 (2022): 2398. http://dx.doi.org/10.1149/ma2022-01412398mtgabs.
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A solid oxide fuel cell (SOFC) converts chemical energy from a fuel gas, such as hydrogen or methane, to electrical energy. Yttria-stabilized zirconia (YSZ) films are often used as electrolytes in which only oxygen ions are carriers. In such cases, the open circuit voltage (OCV = 1.15 V at 1073 K) is equal to the Nernst voltage (Vth = 1.15 V at 1073 K). Samaria-doped ceria (SDC) have higher ionic conductivity. Therefore, SDC films are possible electrolyte candidates. However, when SDC electrolytes are used in SOFCs, the OCV is only 0.80 V at 1073 K. The voltage loss has been explained by Wagner’s equation. Numerous subsequent models have been created based on Wagner’s equation. Using the Riess model, the current-voltage relationship can be calculated with the cathode and anode polarization voltage losses [1]. Furthermore, a nonlinear model was created by Duncan and Wachsman [2]. This model can also be used to explain the equilibrium process. According to the Riess model, the OCV should decrease during electrode degradation. However, experimentally, the OCV does not change during electrode degradation [3]. The change in the equilibration of thick SDC electrolytes in response to a change in the anode gas has never been explained using the model defined by Duncan and Wachsman. Experimentally, when a very thick (6.6 mm) SDC electrolyte is used, the OCV can reach 0.80 V in only 5 minutes [4]. According to Weppner, the corresponding delay in the electron diffusion current should be more than 2080 minutes [5]. We proposed a current-independent anode voltage loss (0.35 V = 1.15 V- 0.80 V) [6]. Since we disproved the existence of large leakage currents in SDC electrolytes, our explanations seem to disregard and disprove Wagner’s equation. However, we noticed that the dismissal of this idea regarding large leakage currents in SDC electrolytes is nothing more than a side effect. When SDC electrolytes experience a large anode voltage loss (0.35 V), the leakage currents are very small. This is called the “anode shielding effect” [7]. The ionic activation energy (Ea) of SDC electrolytes is 0.7 eV (= 0.35 V ×2e). During ion hopping processes in SDC electrolytes, the work done by ions on the surrounding lattice structure is 0.7 eV. The ions should regain the 0.7 eV after hopping. However, when there are many electrons in the hopping path, hopping processes are very complex, and calculating the loss of work is challenging. Jarzynski’s equality is a very useful method of calculating the loss of work only from the first equilibrium state to the second equilibrium state. Because the distribution of hopping ions always should be a canonical ensemble, the loss of work can be calculated. When there are enough electrons, the ions cannot regain the 0.7 eV, and voltage loss (0.35 V) occurs [8]. To assist the above explanation, we use the electromagnetic potential to explain the voltage loss that occurs during ion hopping. We noticed that the potential of ions during hopping can be calculated from the Lorenz gauge condition. Reference: [1] I. Riess, J. Phys. Chem. Solids., 47(2), 129 (1986). doi: 10.1016/0022-3697(86)90121-6. [2] K. L. Duncan and E. D. Wachsman, J. Electrochem. Soc., 156, B1030 (2009). doi: 10.1149/1.315851. [3] T. Miyashita, J. Mater. Sci., 41(10), 3183 (2006). doi: 10.1007/s10853-006-6371-8. [4] T. Miyashita, J. Electrochem. Soc., 164(11) 3190 (2017). doi: 10.1149/2.0251711jes [5] J. Liu and W. Weppner, Ionics, 5(1–2), 115 (1999). doi: 10.1007/BF02375914. [6] T. Miyashita, J. Mater. Sci., 40(22), 6027 (2005). doi: 10.1007/s10855-005-4560-2. [7] B. Dalslet, P. Blennow, P. V. Hendriksen, N. Bonanos, D. Lybye, and M. Mogensen, J. Solid State Electrochem., 10(8), 547 (2006). doi: 10.1007/s10008-006-0135-x. [8] T. Miyashita, Miyashita, ECSarXiv (2020) “Open-Circuit Voltage Anomalies in Yttria-Stabilized Zirconia and Samaria-Doped Ceria Bilayered Electrolytes”, https://ecsarxiv.org/xhn73/
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Yi, Sangwha. "Electromagnetic Field Equation and Lorentz Gauge in Rindler Space-time." December 23, 2016. https://doi.org/10.5281/zenodo.3556148.
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In this paper, we derived electromagnetic field transformations and electromagnetic field equations of Maxwell in Rindler space-time in the context of general theory of relativity. We then treat the Lorentz gauge transformation and the Lorentz gauge fixing condition in Rindler space-time and obtained the transformation of differential operation, the electromagnetic 4-vector potential and the field. In addition, charge density and the electric current density in Rindler spacetime are derived. To view the invariance of the gauge transformation, gauge theory is applied to Maxwell equations in Rindler space-time. In Appendix A, we show that the electromagnetic wave function cannot exist in Rindler space-time. An important point we assert in this article is the uniqueness of the accelerated frame. It is because, in the accelerated frame, one can treat electromagnetic field equations.
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Sangwha, Yi. "Quantization of Electromagnetic Field and Potential in Rindler Space-Time." May 28, 2019. https://doi.org/10.5281/zenodo.3556179.
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The article treats quantization of electromagnetic field that is defined in Rindler space-time. Likely the electromagnetic field, the potential did quantizated in inertial frame, the electromagnetic field, the potential can quantizate by the transformation of electromagnetic field or the transformation of the potential in the accelerated frame. We treat Lorentz gauge condition in quantization of electromagnetic potential.
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Gao, Changjun. "Introduction of the generalized Lorentz gauge condition into the vector-tensor theory." Physical Review D 85, no. 2 (2012). http://dx.doi.org/10.1103/physrevd.85.023533.
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Srivastava, Prem P., and Stanley J. Brodsky. "Light-front formulation of the standard model." August 19, 2002. https://doi.org/10.1103/physrevd.66.045019.
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Light-front (LF) quantization in the light-cone (LC) gauge is used to construct a renormalizable theory of the standard model. The framework derived earlier for QCD is extended to the Glashow-Weinberg-Salam (GWS) model of electroweak interaction theory. The Lorentz condition is automatically satisfied in LF-quantized QCD in the LC gauge for the free massless gauge field. In the GWS model, with the spontaneous symmetry breaking present, we find that the 't Hooft condition accompanies the LC gauge condition corresponding to the massive vector boson. The two transverse polarization vectors for the massive vector boson may be chosen to be the same as found in QCD. The nontransverse and linearly independent third polarization vector is found to be parallel to the gauge direction. The corresponding sum over polarizations in the standard model, indicated by Kμν(k), has several simplifying properties similar to the polarization sum Dμν(k) in QCD. The framework is unitary and ghost free (except for the ghosts at k+=0 associated with the light-cone gauge prescription). The massive gauge field propagator has well-behaved asymptotic behavior. The interaction Hamiltonian of electroweak theory can be expressed in a form resembling that of covariant theory, plus additional instantaneous interactions which can be treated systematically. The LF formulation also provides a transparent discussion of the Goldstone boson (or electroweak) equivalence theorem, as the illustrations show.
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Oettinger, Hans Christian. "Conserved currents for the gauge-field theory with Lorentz symmetry group and a composite theory of gravity." Europhysics Letters, January 25, 2023. http://dx.doi.org/10.1209/0295-5075/acb60d.
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Abstract For the Yang-Mills-type gauge-field theory with Lorentz symmetry group, we propose and verify an explicit expression for the conserved currents in terms of the energy-momentum tensor. A crucial ingredient is the assumption that the gauge symmetry arises from the decomposition of a metric in terms of tetrad variables. The currents exist under the weak condition that the energy-momentum tensor and the Ricci tensor commute. We show how the conserved currents can be used to obtain a composite theory of gravity and discuss the static isotropic field around a point mass at rest.