Teleparallelism as a Gauge Theory for Gravitation
Keywords:
Teleparallelism, Gauge, Yang-Mills, Unification.Abstract
The objective of the present work is to present a theory o gravitation whose formalism is analogous to the other fundamental interactions, which are described by gauge theories. The theory presented is also analogous to general relativity in classical levels. Initially, gauge theories are defined. Electromagnetism is presented as an example of this class of theories. The Dirac and Maxwell lagrangians are defined, and making then invariant by local gauge transformations leads to the sum of a coupling term, which leads to the obtaining of the correct lagrangian for the quantum electrodynamics. Then, the equations associated to the Yang-Mills theory, a gauge theory for special unitary groups of order n, are then presented. After this, the fundamentals of teleparallelism are discussed, which is presented as a gauge theory for the translation group, with the gauge potentials of the model being associated to gravitation. The role of the tetrads and torsion in the description of gravitation is discussed, as well as their geometrical meanings. The teleparallel lagrangian, quadratic in torsion, is then presented, and two applications are explained: a particle under the action of a gravitational field and the question of the energy-momentum density of the gravitational field are presented from the point of view of teleparallel gravity. It follows that teleparallelism, in addition to covering the classical phenomena already treated by general relativity, goes beyond and provides new descriptions, as the definition of a real spacetime and gauge energy momentum tensor for the gravitational field.
References
ANDRADE, V. C. de; GUILLEN, L. C. T.; PEREIRA, J. G. Gravitational Energy-Momentum Density in Teleparallel Gravity . 2000. <https://arxiv.org/pdf/gr-qc/0003100.pdf>. [Acessado em 09/11/2019]. 19, 20
ANDRADE, V. C. de; PEREIRA, J. G. Gravitational Lorentz Force and the Description of the Gravitational Interaction. 1997. <https://arxiv.org/pdf/gr-qc/9703059.pdf>. [Acessado em 03/11/2019]. 3, 11, 12, 13, 17
ANDRADE, V. C. de; PEREIRA, J. G. Riemannian and Teleparallel Descriptions of the Scalar Field Gravitational Interaction . 1997. <https://arxiv.org/pdf/gr-qc/9706070.pdf>. [Acessado em 08/11/2019]. 18
ANTONY, L. Ficheiro:Parallel_transport.png. 2006. <https://commons.wikimedia.org/wiki/File:Parallel_transport.png>. [Acessado em 30/09/2019]. 15
BATTERMAN, R. W. The Oxford Handbook of Philosophy of Physics. [S.l.]: Oxford University Press, 2013. 3
BOSSO, P. Generalized Uncertainty Principle and Quantum Gravity Phenomenology . 2017 <https://arxiv.org/pdf/1709.04947.pdf>. [Acessado em 29/07/2018]. 2
BURGESS, C. P. Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory. 2003. <https://arxiv.org/abs/gr-qc/0311082>. [Acessado em 23/07/2018]. 2
CARROLL, S. Spacetime and Geometry - An Introduction to General Relativity. [S.l.]: Addison Wesley, 2004. 14
DUFF, M. J. M-Theory (the Theory Formerly Known as Strings). 1996. <https://arxiv.org/abs/hep-th/9608117>. [Acessado em 14/02/2020]. 3
JAKOB. Fiber Bundles. 2018. <https://physicstravelguide.com/advanced_tools/fiber_bundles>. [Acessado em 18/10/2019]. 4
KALUZA, T. On the Unification Problem in Physics. 1921. <https://arxiv.org/abs/1503.03695>.[Acessado em 14/02/2020]. 3
KASUGAHUANG. File:Torsion along a geodesic.svg. 2007. <https://en.wikipedia.org/wiki/File:Torsion_along_a_geodesic.svg>. [Acessado em 07/11/2019]. 15
MALUF, J. W.; ROCHA-NETO, J. F. da. Hamiltonian formulation of general relativity in the teleparallel geometry. Physical Review D, v. 64, 09 2001. Disponível em: <https://journals.aps.org/prd/abstract/10.1103/PhysRevD.64.084014>. Acesso em: 11 nov. 2019. 3, 10
MALUF, J. W.; ROCHA-NETO, J. F. da; ULHOA, S. C. Bondi-Sachs energy-momentum and the energy of gravitational radiation. 2015. <https://arxiv.org/abs/1503.03695>. [Acessado em 14/02/2020]. 3
PEREIRA, J. G.; ALDROVANDI, R. An Introduction to Geometrical Physics. [S.l.]: World Scientific, 1995. 7
PEREIRA, J. G.; ALDROVANDI, R. An Introduction to Teleparallel Gravity. 2010. <http://www.ift.unesp.br/users/jpereira/classnotes.html>. [Acessado em 22/03/2019]. 2, 3
PEREIRA, J. G.; ALDROVANDI, R. Teleparallel Gravity - An Introduction. [S.l.]: Springer, 2013. 4, 7
ROVELLI, C. Loop Quantum Gravity. 1997. <https://arxiv.org/abs/gr-qc/9710008>. [Acessado em 14/02/2020]. 3
SCHWARZ, J. H.; SEIBERG, N. String Theory, Supersymmetry, Unification, and All That. 1998. <https://arxiv.org/abs/hep-th/9803179>. [Acessado em 14/02/2020]. 3
SCHWICHTENBERG, J. Physics from Symmetry. [S.l.]: Springer, 2018. 4, 5, 6
UNZICKER, A.; CASE, T. Translation of Einstein’s Attempt of a Unified Field Theory with Teleparallelism. 2005. 1-3 p. <https://arxiv.org/pdf/physics/0503046.pdf>. [Acessado em 10/06/2019]. 3
Downloads
Published
Issue
Section
License
Copyright (c) 2020 Physicae Organum
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Autores que publicam nesta revista concordam com os seguintes termos:
Autores mantém os direitos autorais e concedem à revista o direito de primeira publicação, sendo o trabalho simultaneamente licenciado sob a Creative Commons Attribution License o que permite o compartilhamento do trabalho com reconhecimento da autoria do trabalho e publicação inicial nesta revista.
Autores têm autorização para assumir contratos adicionais separadamente, para distribuição não-exclusiva da versão do trabalho publicada nesta revista (ex.: publicar em repositório institucional ou como capítulo de livro), com reconhecimento de autoria e publicação inicial nesta revista.
Autores têm permissão e são estimulados a publicar e distribuir seu trabalho online (ex.: em repositórios institucionais ou na sua página pessoal) a qualquer ponto antes ou durante o processo editorial, já que isso pode gerar alterações produtivas, bem como aumentar o impacto e a citação do trabalho publicado (Veja O Efeito do Acesso Livre).
