The spin-torsion sector of a new gauge-theoretic formulation of gravity is analysed 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 analogues of the Einstein-Cartan-Dirac equations. Finally, a semi-classical model for a spinning point-particle moving in a gravitational background with torsion is considered.
C.J.L Doran, A.N. Lasenby, A.D. Challinor and S.F. Gull, Effects of spin-torsion in gauge theory gravity, J. Math. Phys. 39(6), 3303–3321 (1998)