Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity—Prospects for Unified Field Theories
Abstract
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 nonEuclidean, postRiemannian spacetime geometries, providing the adequate formalism for metricaffine theories of gravity with curvature, torsion and nonmetricity. 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 EinsteinCartanSciamaKibble theory, the teleparallel equivalent of general relativity, quadratic metricaffine Lagrangians, nonLorentzian connections, and the breaking of Lorentz invariance in the presence of nonmetricity. We also highlight the probing of postRiemannian 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.
 Publication:

Universe
 Pub Date:
 December 2020
 DOI:
 10.3390/universe6120238
 arXiv:
 arXiv:2012.06356
 Bibcode:
 2020Univ....6..238C
 Keywords:

 gauge field theory;
 YangMills fields;
 modified gravity;
 nonRiemannian geometry;
 spacetime symmetries;
 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena;
 High Energy Physics  Theory
 EPrint:
 33 pages. Invite review to the Special Issue "80 Years of Professor Wigner's Seminal Work "On Unitary Representations of the Inhomogeneous Lorentz Group"". Matches published version