On Einstein-Cartan Theory: I. Kinematical description

TL;DR

This paper develops a Hamiltonian formulation of Einstein-Cartan theory, deriving equations of motion without fixing the coframe, and analyzes constraints and phase space reduction in a Lorentz gauge framework.

Contribution

It introduces a 3+1 decomposition for Einstein-Cartan theory that preserves Lorentz gauge freedom and provides a detailed Hamilton-Dirac analysis including constraints and phase space reduction.

Findings

Derived equations of motion for gravitational connection and coframe

Analyzed second class constraints and defined Dirac brackets

Performed phase space reduction and introduced canonical coordinates

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.