Relevant bibliographies by topics / +3 covariant formalism

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Academic literature on the topic '+3 covariant formalism'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "+3 covariant formalism"

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GOURGOULHON, E., and J. NOVAK. "COVARIANT CONFORMAL DECOMPOSITION OF EINSTEIN EQUATIONS." International Journal of Modern Physics A 17, no. 20 (August 10, 2002): 2762. http://dx.doi.org/10.1142/s0217751x02011898.

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It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-"metric" (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this "metric", of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.
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Miramontes, T., and D. Sudarsky. "El formalismo 3+1 en relatividad general y la descomposición tensorial completa." Revista Mexicana de Física E 64, no. 2 (June 11, 2018): 108. http://dx.doi.org/10.31349/revmexfise.64.108.

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A brief review of 3 + 1 formalism in General Relativity is presented, introducing innovative conventions and notation elements which make it easier to deal with all of the tensorial projections involved in this formalism. Also, useful 3 + 1 expressions for manipulation of indexes (contraction, symmetrization, anti-symmetrization), tensorial producs and the covariant derivative of arbitrary tensors are obtained.
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HAYASHI, MITSUO J. "SPIN-3/2 FERMIONS IN TWISTOR FORMALISM." Modern Physics Letters A 16, no. 32 (October 20, 2001): 2103–13. http://dx.doi.org/10.1142/s0217732301005412.

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Consistency conditions for the local existence of massless spin-3/2 fields have been explored to find the facts that the field equations for massless helicity-3/2 particles are consistent if the space–time is Ricci-flat, and that in Minkowski space–time the space of conserved charges for the fields is its twistor space itself. After considering the twistorial methods to study such massless helicity-3/2 fields, we show in flat space–time that the charges of spin-3/2 fields, defined topologically by the first Chern number of their spin-lowered self-dual Maxwell fields, are given by their twistor space, and in curved space–time that the (anti-)self-duality of the space–time is the necessary condition. Since in N=1 supergravity torsions are the essential ingredients, we generalize our space–time to that with torsion (Einstein–Cartan theory), and investigate the consistency of existence of spin-3/2 fields in this theory. A simple solution to this consistency problem is found: The space–time has to be conformally (anti-)self-dual, left-(or right-) torsion-free. The integrability condition on α-surface shows that the (anti-)self-dual Weyl spinor can be described only by the covariant derivative of the right-(left-)handed torsion.
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Foussats, A., and O. Zandron. "Wess-Zumino supermultiplet coupled to supergravity in a covariant Hamiltonia formalism." Annals of Physics 189, no. 1 (January 1989): 174–89. http://dx.doi.org/10.1016/0003-4916(89)90083-3.

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Balachandran, A. P., Arshad Momen, and Amilcar R. de Queiroz. "Equations of motion as covariant Gauss law: The Maxwell–Chern–Simons case." Modern Physics Letters A 32, no. 25 (July 31, 2017): 1750133. http://dx.doi.org/10.1142/s0217732317501334.

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Time-independent gauge transformations are implemented in the canonical formalism by the Gauss law which is not covariant. The covariant form of Gauss law is conceptually important for studying the asymptotic properties of the gauge fields. For QED in 3 + 1 dimensions, we have developed a formalism for treating the equations of motion (EOM) themselves as constraints, that is, constraints on states using Peierls’ quantization.1 They generate spacetime dependent gauge transformations. We extend these results to the Maxwell–Chern–Simons (MCS) Lagrangian. The surprising result is that the covariant Gauss law commutes with all observables: the gauge invariance of the Lagrangian gets trivialized upon quantization. The calculations do not fix a gauge. We also consider a novel gauge condition on the test functions (not on quantum fields) which we name the “quasi-self-dual gauge” condition. It explicitly shows the mass spectrum of the theory. In this version, no freedom remains for the gauge transformations: EOM commute with all observables and are in the center of the algebra of observables.
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AHLUWALIA, D. V., and D. J. ERNST. "(j, 0) ⊕ (0, j) COVARIANT SPINORS AND CAUSAL PROPAGATORS BASED ON WEINBERG FORMALISM." International Journal of Modern Physics E 02, no. 02 (June 1993): 397–422. http://dx.doi.org/10.1142/s0218301393000145.

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A pragmatic approach to constructing a covariant phenomenology of the interactions of composite high-spin hadrons is proposed. Because there are no known wave equations without significant problems, we propose to construct the phenomenology without explicit reference to a wave equation. This is done by constructing the individual pieces of a perturbation theory and then utilizing the perturbation theory as the definition of the phenomenology. The covariant spinors for a particle of spin j are constructed directly from Lorentz invariance and the basic precepts of quantum mechanics following the logic put forth originally by Wigner and developed by Weinberg. Explicit expressions for the spinors are derived for j=1, 3/2 and 2. Field operators are constructed from the spinors and the free-particle propagator is derived from the vacuum expectation value of the time-order product of the field operators. A few simple examples of model interactions are given. This provides all the necessary ingredients to treat at a phenomenological level and in a covariant manner particles of arbitrary spin.
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Rogalyov, R. N. "The uses of covariant formalism in analytical computation of Feynman diagrams with massive fermions." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 502, no. 2-3 (April 2003): 602–4. http://dx.doi.org/10.1016/s0168-9002(03)00516-3.

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Shah, Mushtaq Bashir, and Prince Ahmad Ganai. "A study of 3-form gauge theories in the Lorentz violating background." International Journal of Geometric Methods in Modern Physics 15, no. 07 (May 24, 2018): 1850106. http://dx.doi.org/10.1142/s0219887818501062.

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We study the Lorentz symmetry breaking of the 3-form gauge theory down to its sub-group. A 3-form gauge theory is studied in such a Lorentz violating background and these symmetry violation effects will affect the aspects of such a gauge theory. Also, we study the gaugeon formalism and FFBRST of 3-form theory in such a background. It is seen that the generating functional gets modified. With this, we obtain a connection between covariant and noncovariant gauges of such a gauge theory. Furthermore, we study the Batalin–Vilkovisky (BV) formulation of such a gauge theory in such a Lorentz violating background.
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Sherif, Abbas, Rituparno Goswami, and Sunil D. Maharaj. "Marginally trapped surfaces in null normal foliation spacetimes: A one step generalization of LRS II spacetimes." International Journal of Geometric Methods in Modern Physics 17, no. 07 (May 26, 2020): 2050097. http://dx.doi.org/10.1142/s0219887820500978.

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In this paper, we study geometrical properties of marginally trapped surfaces in gravitational collapse, using a semi-tetrad covariant formalism, that provides a set of geometrical and matter variables. We first define a generalization (in a sense to be specified in the introduction) of LRS II spacetime — which we call NNF spacetimes — and show that the marginally trapped surfaces in NNF spacetimes (and the 3-surfaces they foliate) are topologically equivalently those of LRS II spacetimes. We then study the evolution of MTTs (3-surfaces foliated by marginally trapped surfaces), extending earlier work on LRS II spacetimes to NNF spacetimes, and in general any 4-dimensional spacetime. In addition, we perform a stability analysis for the marginally trapped surfaces in this formalism, using simple spacetimes as examples to demonstrate the applicability of our approach.
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Ntahompagaze, Joseph, Amare Abebe, and Manasse Mbonye. "A study of perturbations in scalar–tensor theory using 1 + 3 covariant approach." International Journal of Modern Physics D 27, no. 03 (February 2018): 1850033. http://dx.doi.org/10.1142/s0218271818500335.

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This work discusses scalar–tensor theories of gravity, with a focus on the Brans–Dicke sub-class, and one that also takes note of the latter’s equivalence with [Formula: see text] gravitation theories. A [Formula: see text] covariant formalism is used in this case to discuss covariant perturbations on a background Friedmann–Laimaître–Robertson–Walker (FLRW) spacetime. Linear perturbation equations are developed based on gauge-invariant gradient variables. Both scalar and harmonic decompositions are applied to obtain second-order equations. These equations can then be used for further analysis of the behavior of the perturbation quantities in such a scalar–tensor theory of gravitation. Energy density perturbations are studied for two systems, namely for a scalar fluid-radiation system and for a scalar fluid-dust system, for [Formula: see text] models. For the matter-dominated era, it is shown that the dust energy density perturbations grow exponentially, a result which agrees with those already existing in the literatures. In the radiation-dominated era, it is found that the behavior of the radiation energy–density perturbations is oscillatory, with growing amplitudes for [Formula: see text], and with decaying amplitudes for [Formula: see text]. This is a new result.
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Dissertations / Theses on the topic "+3 covariant formalism"

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Jönsson, Johan. "Non-isotropic Cosmology in 1+3-formalism." Thesis, Linköpings universitet, Matematiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-113269.

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Cosmology is an attempt to mathematically describe the behaviour of the universe, the most commonly used models are the Friedmann-Lemaître-Robertson-Walker solutions. These models seem to be accurate for an old universe, which is homogeneous with low anisotropy. However for an earlier universe these models might not be that accurate or even correct. The almost non-existent anisotropy observed today might have played a bigger role in the earlier universe. For this reason we will study another model known as Bianchi Type I, where the universe is not necessarily isotropic. We utilize a 1+3-covariant formalism to obtain the equations that determine the behaviour of the universe and then use a tetrad formalism to complement the 1+3-covariant equations. Using these equations we examine the geometry of space-time and its dynamical properties. Finally we briefly discuss the different singularities possible and examine some special cases of geodesic movement.
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Menadeo, Nicola. "Formalismo 3+1 ed approccio hamiltoniano alla relatività generale." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14602/.

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Nel primo capitolo di questo elaborato verranno descritti ed analizzati alcuni concetti di base della geometria differenziale generalizzandoli a spazi a dimensione arbitraria, per poi utilizzarli nel caso specifico dello spazio-tempo quadridimensionale in cui opera la relatività generale. Verrà fatto largo uso della nozione di ipersuperficie, fondamentale per l'approccio matematico al formalismo 3+1 e verrà studiato il modo in cui questa evolve, da cui segue il concetto di foliazione dello spazio-tempo. Lo scopo finale sarà quello di decomporre i tensori di Riemann e Ricci che giocano un ruolo centrale nella equazione di campo di Einstein. Il secondo capitolo invece, sarà incentrato sulla fisica e su come il formalismo 3+1 agisce nella teoria della relatività generale. L'argomento principale sarà la decomposizione dell'equazione di Einstein che verrà successivamente trattata come un sistema di equazioni differenziali alle derivate parziali. Sarà introdotto ed utilizzato il concetto di geometrodinamica (introdotto da Wheeler nei primi anni sessanta) per giungere all'approccio hamiltoniano alla relatività generale.
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Holgersson, David. "Lanczos potentialer i kosmologiska rumtider." Thesis, Linköping University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2582.

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We derive the equation linking the Weyl tensor with its Lanczos potential, called the Weyl-Lanczos equation, in 1+3 covariant formalism for perfect fluid Bianchi type I spacetime and find an explicit expression for a Lanczos potential of the Weyl tensor in these spacetimes. To achieve this, we first need to derive the covariant decomposition of the Lanczos potential in this formalism. We also study an example by Novello and Velloso and derive their Lanczos potential in shear-free, irrotational perfect fluid spacetimes from a particular ansatz in 1+3 covariant formalism. The existence of the Lanczos potential is in some ways analogous to the vector potential in electromagnetic theory. Therefore, we also derive the electromagnetic potential equation in 1+3 covariant formalism for a general spacetime. We give a short description of the necessary tools for these calculations and the cosmological formalism we are using.

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Book chapters on the topic "+3 covariant formalism"

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Rovelli, Carlo. "Dynamics without Time for Quantum Gravity: Covariant Hamiltonian Formalism and Hamilton-Jacobi Equation on the Space G." In Decoherence and Entropy in Complex Systems, 36–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-40968-7_4.

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