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 TMF, 2018, Volume 195, Number 2, Pages 313–328 (Mi tmf9413)

Dynamical symmetry breaking in geometrodynamics

A. Garat

Physics Institute, Department of Sciences, University of the Republic, Montevideo, Uruguay

Abstract: Using a first-order perturbative formulation, we analyze the local loss of symmetry when a source of electromagnetic and gravitational fields interacts with an agent that perturbs the original geometry associated with the source. We had proved that the local gauge groups are isomorphic to local groups of transformations of special tetrads. These tetrads define two orthogonal planes at every point in space–time such that every vector in these local planes is an eigenvector of the Einstein–Maxwell stress–energy tensor. Because the local gauge symmetry in Abelian or even non-Abelian field structures in four-dimensional Lorentzian space–times is manifested by the existence of local planes of symmetry, the loss of symmetry is manifested by a tilt of these planes under the influence of an external agent. In this strict sense, the original local symmetry is lost. We thus prove that the new planes at the same point after the tilting generated by the perturbation correspond to a new symmetry. Our goal here is to show that the geometric manifestation of local gauge symmetries is dynamical. Although the original local symmetries are lost, new symmetries arise. This is evidence for a dynamical evolution of local symmetries. We formulate a new theorem on dynamical symmetry evolution. The proposed new classical model can be useful for better understanding anomalies in quantum field theories.

Keywords: new group, new group isomorphism, Einstein–Maxwell gauge symmetry, perturbative formulation, dynamical symmetry breaking.

DOI: https://doi.org/10.4213/tmf9413

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English version:
Theoretical and Mathematical Physics, 2018, 195:2, 764–776

Bibliographic databases:

Citation: A. Garat, “Dynamical symmetry breaking in geometrodynamics”, TMF, 195:2 (2018), 313–328; Theoret. and Math. Phys., 195:2 (2018), 764–776

Citation in format AMSBIB
\Bibitem{Gar18} \by A.~Garat \paper Dynamical symmetry breaking in geometrodynamics \jour TMF \yr 2018 \vol 195 \issue 2 \pages 313--328 \mathnet{http://mi.mathnet.ru/tmf9413} \crossref{https://doi.org/10.4213/tmf9413} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2018TMP...195..764G} \elib{http://elibrary.ru/item.asp?id=32823077} \transl \jour Theoret. and Math. Phys. \yr 2018 \vol 195 \issue 2 \pages 764--776 \crossref{https://doi.org/10.1134/S0040577918050100} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000434491300010} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048268601} 

• http://mi.mathnet.ru/eng/tmf9413
• https://doi.org/10.4213/tmf9413
• http://mi.mathnet.ru/eng/tmf/v195/i2/p313

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This publication is cited in the following articles:
1. Garat A., “Tetrads in Low-Energy Weak Interactions”, Int. J. Mod. Phys. A, 33:33 (2018), 1850197
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