| Two extensions of Einstein's general theory of relativity (GR) are fused together (higher derivative theory and torsion) in an attempt to construct models of propagating torsion. When the standard model of GR is generalized to include torsion the field equations have only the trivial solution for the torsion field. In the presence of spinors the field equations imply that the totally antisymmetric part of the torsion tensor (TAST) is proportional to the spin density. Resent advances in torsion field theory suggest the use of a modified volume element. The models constructed in this text use terms in the action that are quadratic in the curvature tensors to produce torsion dynamics. The case of TAST is worked out in four dimensions and is shown to be equivalent to the Proca field minimally coupled to gravity. Torsion field theory in three and two dimensions is also discussed.;In addition to the modeling of propagating torsion the existence of an internal symmetry of the space-time connection is demonstrated and its consequences discussed. The effects of torsion of geodesic deviation are worked out and finally the Anowitt, Deser, Misner (ADM) split is performed on the metric and the Hamiltonian calculated in the presence of a dynamic torsion theory. |
