Academic literature on the topic 'Lorentz Gauge condition'
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Journal articles on the topic "Lorentz Gauge condition"
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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.
Dissertations / Theses on the topic "Lorentz Gauge condition"
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Dzimida-Chmielewska, Elżbieta. "Symetria cechowania i transformacja Lorentza dla 2-punktowych funkcji Wightmana w elektrodynamice kwantowej dla 2-potencjałowego modelu Zwanzigera." Phd thesis, 2014. http://hdl.handle.net/11320/1313.
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Wydział Fizyki.<br>W pracy przedstawiono opis sektora pól cechowania dla elektrodynamiki kwantowej z prądami elektrycznymi i magnetycznymi. Wykorzystano model Zwanzigera zawierający dwa niezależne potencjały cechowania i . Założono, że prądy elektryczne i magnetyczne mają takie same własności transformacyjne, co prowadzi do złamania symetrii i , a jedynie złożenie transformacji lub ogólniej jest symetrią układu. Dla pól cechowania, badano własności 2-punktowej funkcji Wightmana, czyli próżniowej wartości oczekiwanej dla nieuporządkowanego iloczynu dwóch operatorów pola cechowania. Pokazano ogólną postać diagonalnych funkcji Wightmana, i dla różnych warunków cechowania, która ma postać symetryczną i zawiera część niezmienniczą proporcjonalną do . Ponadto znaleziono równanie różniczkowe na mieszane funkcje Wightmana i wykazano, że nie ma ono lorentzowsko-niezmienniczego rozwiązania. Znaleziono sferycznie symetryczne rozwiązanie, które odpowiada cechowaniu Coulomba, co zostało udowodnione na drodze kanonicznego kwantowania metodą Diraca. Dla innych warunków cechowania: planarnym, cechowaniu stożka świetlnego w kierunku oraz , została przeprowadzona procedura kwantowania kanonicznego metodą Faddeeva-Jackiwa. Wyznaczone funkcje Wightmana w tych cechowaniach są zgodne z ogólnymi wzorami, wyprowadzonymi wcześniej i znaleziono postać członów zależnych od cechowania.<br>This dissertation analyses the gauge field sector for the quantum electrodynamics with electric and magnetic currents. It uses the Zwanziger model with two independent gauge field potentials and . The assumption that the electric and magnetic currents have the same transformation properties, effectively leads to the and symmetry breaking, while the composed transformation or generally recovers the symmetry of the system. The properties of two-point Wightman functions, i.e. the vacuum expectations values of the unordered product two gauge field operators, were intensively studied. The general form of the diagonal Wightman functions and is found for different choices of gauge fixing conditions - it has a symmetrical form and includes the invariant part proportional to . Furthermore, the differential equation has been found for the mixed Wightman functions . It is shown that this equation has no Lorentz covariant solution. But the spherically symmetric solution has been found and it corresponds to the Coulomb gauge condition - this is proven by the canonical quantization procedure for systems with constraints - the Dirac method. For other gauge conditions: planar, light cone gauge in end direction, the canonical quantization procedure is carried out within the simplified procedure - the Faddeev-Jackiw method. The Wightman functions for the gauge field potentials are found and they are consistent with general formulas derived before. Also the gauge dependent parts are explicitly given for different gauge fixing conditions.
Book chapters on the topic "Lorentz Gauge condition"
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Dzimida-Chmielewska, Elżbieta, and Jerzy A. Przeszowski. "Physical and Nonphysical Modes in the Light Front Formulation for the LC Gauge and the Lorentz Gauge Conditions." In Light Cone 2016. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65732-5_33.
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CRONSTRöM, C. "A Simple and Complete Lorentz-Covariant Gauge Condition." In Current Physics–Sources and Comments. Elsevier, 1992. http://dx.doi.org/10.1016/b978-0-444-89745-9.50012-4.
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Freeman, Richard, James King, and Gregory Lafyatis. "The Potentials." In Electromagnetic Radiation. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198726500.003.0002.
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The concepts of scalar and vector potentials are introduced and the electric and magnetic fields are shown to be derived from specific forms of these potentials. The choice of these forms is restricted by gauge considerations, and the Lorenz gauge is introduced as the one most applicable for radiation. Using this, the wave equations prescribing the potentials in terms of the source conditions are presented. The modifications of vector and scalar potentials to account for speed of light and causality lead to the concept of “retarded time.” The potentials can be expressed in terms of moments of the source along with concepts of “near,” “intermediate,” and “far” zones to facilitate derivation of approximate expressions for the potentials evaluated at appropriate distances from the source. Finally, expressions for the vector potential in terms of the electric and magnetic dipole, and electric quadrupole moments of the source in the approximation zones are presented.
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I. Arbab, Arbab. "Quantum Electrodynamics of Massive Bosons." In Electromagnetic Field - From Atomic Level to Engineering Applications [Working Title]. IntechOpen, 2025. https://doi.org/10.5772/intechopen.1010422.
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This chapter presents a novel theoretical framework that extends quantum electrodynamics to incorporate massive bosons using a quaternionic formalism. By modifying Maxwell’s equations to include a mass term, the study reveals that massive bosons exhibit unique electromagnetic properties: They can sustain a nonzero electric field even when the magnetic field vanishes under suitable gauge transformations. Unlike traditional electrodynamics, which strictly follows the Lorenz gauge condition, this formulation highlights the essential role of boson mass in defining quantum energy and momentum densities. It naturally leads to field equations that satisfy the Klein-Gordon equation and demonstrates a deep equivalence between particle and wave momentum, reinforcing wave-particle duality. The framework predicts novel effects, such as classical Hall conductivity without an external magnetic field and a quantized Hall effect in two-dimensional electron gases (2DEGs). It suggests that phenomena like quantum inductance, critical currents, and quantized capacitance can be directly linked to the mass and spin of bosons. Additionally, the theory introduces gauge-spin transformations that couple spin and helicity densities to the boson’s mass, offering new perspectives on energy-momentum conservation in electromagnetic systems. The model aligns with the established theories, including Wilczek’s axion electrodynamics and the Proca formulation, while opening new experimental possibilities in condensed matter physics, particularly in the study of topological insulators and low-dimensional systems. Overall, this comprehensive framework bridges classical and quantum electrodynamics, providing a unified description of massive boson behavior and a foundation for future theoretical and experimental exploration in modern quantum field theory.
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Dyall, Kenneth G., and Knut Faegri. "Molecular Properties." In Introduction to Relativistic Quantum Chemistry. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780195140866.003.0019.
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Strictly speaking, in quantum mechanics a measurable property is defined as an observable connected to a self-adjoint operator. However, in common usage the term molecular property is loosely taken to mean any physical attribute of a molecule, preferably amenable to experimental measurement. Common examples of properties of interest to chemists are molecular structure, thermodynamic quantities, spectroscopic transition energies and intensities, and various electric and magnetic moments. The amenability to experiment may exist only in principle—one of the strong points of modern computational chemistry is the possibility of studying phenomena occurring under conditions that lie beyond the present experimental capabilities. Sometimes, differential effects between different theoretical models are also regarded as properties: thus the correlation energy is generally considered to be the difference between the Hartree–Fock energy and the energy obtained from a complete many-electron treatment (e.g. full CI or MBPT to all orders). At best only the latter of these is accessible to experiment. Similarly, certain relativistic effects (e.g. bond contraction) only appear as the difference between results from a relativistic and a nonrelativistic calculation. The calculation of molecular properties in a relativistic framework follows the same principles as for the nonrelativistic case once a wave function or electron density of adequate quality is available. Our aim here is therefore not to provide explicit expressions and formulas for the calculation of a more or less complete catalog of properties. However, in relativistic calculations of molecular properties there are some aspects of the theory that warrant special care and consideration. In particular, we need to know how to handle features such as Lorentz invariance, gauge invariance, and negativeenergy states. Moreover, the electric and magnetic fields appear as natural parts of the relativistic Hamiltonian, and we therefore expect that properties involving these may require a different treatment from the nonrelativistic case where terms involving external fields are grafted onto the nonrelativistic Hamiltonian, often based on some reduction or approximation from the relativistic case.