Effects of spin-torsion in gauge theory gravity

Abstract

The spin-torsion sector of a new gauge-theoretic formulation of gravity is analyzed and the relationship to the Einstein–Cartan–Kibble–Sciama theory of gravity is discussed. The symmetries of the Riemann tensor and the conservation laws of the theory are derived. This formalism is applied to the problem of a Dirac field coupled self-consistently to gravity. The equations derived from a minimally coupled gauge-invariant Lagrangian naturally give the gauge-theoretic analogs of the Einstein–Cartan–Dirac equations. Finally, a semiclassical model for a spinning point-particle moving in a gravitational background with torsion is considered.