On Einstein-Cartan Theory: I. Kinematical description

Abstract

Equations of motion for general gravitational connection and orthonormal coframe from the Einstein-Hilbert type action are derived. Our formulation does not fix coframe to be tangential to spatial section hence Lorentz group is still present as a part of gauge freedom. 3+1 decomposition introduces tangent Minkowski structures hence Hamilton-Dirac approach to dynamics works with Lorentz connection over the spatial section. The second class constraints are analyzed and Dirac bracket is defined. Reduction of the phase space is performed and canonical coordinates are introduced.