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Review

Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity—Prospects for Unified Field Theories

1
Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa, Edifício C8, Campo Grande, P-1749-016 Lisbon, Portugal
2
Departamento de Física Teórica and IPARCOS, Universidad Complutense de Madrid, E-28040 Madrid, Spain
*
Author to whom correspondence should be addressed.
Universe 2020, 6(12), 238; https://doi.org/10.3390/universe6120238
Received: 13 November 2020 / Revised: 7 December 2020 / Accepted: 7 December 2020 / Published: 11 December 2020
Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime geometries, providing the adequate formalism for metric-affine theories of gravity with curvature, torsion and non-metricity. In this paper, we analyze the structure of gauge theories of gravity and consider the relation between fundamental geometrical objects and symmetry principles as well as different spacetime paradigms. Special attention is given to Poincaré gauge theories of gravity, their field equations and Noether conserved currents, which are the sources of gravity. We then discuss several topics of the gauge approach to gravitational phenomena, namely, quadratic Poincaré gauge models, the Einstein-Cartan-Sciama-Kibble theory, the teleparallel equivalent of general relativity, quadratic metric-affine Lagrangians, non-Lorentzian connections, and the breaking of Lorentz invariance in the presence of non-metricity. We also highlight the probing of post-Riemannian geometries with test matter. Finally, we briefly discuss some perspectives regarding the role of both geometrical methods and symmetry principles towards unified field theories and a new spacetime paradigm, motivated from the gauge approach to gravity. View Full-Text
Keywords: gauge field theory; Yang-Mills fields; modified gravity; non-Riemannian geometry; spacetime symmetries gauge field theory; Yang-Mills fields; modified gravity; non-Riemannian geometry; spacetime symmetries
MDPI and ACS Style

Cabral, F.; Lobo, F.S.N.; Rubiera-Garcia, D. Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity—Prospects for Unified Field Theories. Universe 2020, 6, 238. https://doi.org/10.3390/universe6120238

AMA Style

Cabral F, Lobo FSN, Rubiera-Garcia D. Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity—Prospects for Unified Field Theories. Universe. 2020; 6(12):238. https://doi.org/10.3390/universe6120238

Chicago/Turabian Style

Cabral, Francisco, Francisco S.N. Lobo, and Diego Rubiera-Garcia. 2020. "Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity—Prospects for Unified Field Theories" Universe 6, no. 12: 238. https://doi.org/10.3390/universe6120238

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