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A gauge-theoretic approach to gravity

Einstein's general relativity (GR) is a dynamical theory of the space–time metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearized level and show how a gauge-theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a mu...

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Detalles Bibliográficos
Autor principal: Krasnov, Kirill
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society Publishing 2012
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3390791/
https://www.ncbi.nlm.nih.gov/pubmed/22792040
http://dx.doi.org/10.1098/rspa.2011.0638
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description Einstein's general relativity (GR) is a dynamical theory of the space–time metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearized level and show how a gauge-theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a much more simple and compact form than in the standard metric description. Moreover, in contrast to the GR situation, the gauge theory Lagrangian is convex. We then proceed with a formulation of the full nonlinear theory. The equivalence to the metric-based GR holds only at the level of solutions of the field equations, that is, on-shell. The gauge-theoretic approach also makes it clear that GR is not the only interacting theory of massless spin two particles, in spite of the GR uniqueness theorems available in the metric description. Thus, there is an infinite-parameter class of gravity theories all describing just two propagating polarizations of the graviton. We describe how matter can be coupled to gravity in this formulation and, in particular, how both the gravity and Yang–Mills arise as sectors of a general diffeomorphism-invariant gauge theory. We finish by outlining a possible scenario of the ultraviolet completion of quantum gravity within this approach.
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spelling pubmed-33907912012-07-12 A gauge-theoretic approach to gravity Krasnov, Kirill Proc Math Phys Eng Sci Review Articles Einstein's general relativity (GR) is a dynamical theory of the space–time metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearized level and show how a gauge-theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a much more simple and compact form than in the standard metric description. Moreover, in contrast to the GR situation, the gauge theory Lagrangian is convex. We then proceed with a formulation of the full nonlinear theory. The equivalence to the metric-based GR holds only at the level of solutions of the field equations, that is, on-shell. The gauge-theoretic approach also makes it clear that GR is not the only interacting theory of massless spin two particles, in spite of the GR uniqueness theorems available in the metric description. Thus, there is an infinite-parameter class of gravity theories all describing just two propagating polarizations of the graviton. We describe how matter can be coupled to gravity in this formulation and, in particular, how both the gravity and Yang–Mills arise as sectors of a general diffeomorphism-invariant gauge theory. We finish by outlining a possible scenario of the ultraviolet completion of quantum gravity within this approach. The Royal Society Publishing 2012-08-08 2012-03-21 /pmc/articles/PMC3390791/ /pubmed/22792040 http://dx.doi.org/10.1098/rspa.2011.0638 Text en This journal is © 2012 The Royal Society http://creativecommons.org/licenses/by/3.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Review Articles
Krasnov, Kirill
A gauge-theoretic approach to gravity
title A gauge-theoretic approach to gravity
title_full A gauge-theoretic approach to gravity
title_fullStr A gauge-theoretic approach to gravity
title_full_unstemmed A gauge-theoretic approach to gravity
title_short A gauge-theoretic approach to gravity
title_sort gauge-theoretic approach to gravity
topic Review Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3390791/
https://www.ncbi.nlm.nih.gov/pubmed/22792040
http://dx.doi.org/10.1098/rspa.2011.0638
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