The gauge treatment of gravity

Abstract

The gauge gravitation theory, in spite of twenty five years of its history, still remains the single gap in the excellent gauge picture of fundamental interactions. The main disputable point is the gauge status of Einstein's gravitational field, which is a metric or tetrad field, while gauge fields represent connections on fiber bundles. The corner-stones of Einstein's gravitation theory are the Relativity and Equivalence Principles. Having been reformulated in the fiber bundle terms, the gravitation theory turns out to be built from these principles directly as a gauge theory of space-time symmetries, which, however, are spontaneously broken down to the Lorentz symmetries. Metric gravitational fields appear in such a theory as the consequence of this spontaneous symmetry breaking and have the nature of Goldstone type fields. The Lorentz, GL(4, R) and Poincaré gauge theories of gravitation are analyzed from these points of view, and some outlooks of the gauge treatment of gravitation, e.g., as the affine-metric theory, are discussed.