Classical gauge theory of gravity

Abstract

The classical theory of gravity is formulated as a gauge theory on a frame bundle with spontaneous symmetry breaking caused by the existence of Dirac fermionic fields. The pseudo-Riemannian metric (tetrad field) is the corresponding Higgs field. We consider two variants of this theory. In the first variant, gravity is represented by the pseudo-Riemannian metric as in general relativity theory; in the second variant, it is represented by the effective metric as in the Logunov relativistic theory of gravity. The configuration space, Dirac operator, and Lagrangians are constructed for both variants.