Dirac consistency of the algebra of Hamiltonian constraints in reduced 4-D general relativity

TL;DR

This paper introduces a new Dirac-consistent action for a sector of 4-D general relativity where the Hamiltonian constraints form a first class algebra, linking it to Ashtekar and spin connection formulations.

Contribution

It provides a stand-alone, Dirac-consistent action with two degrees of freedom per point, and details the transformation to and from Ashtekar and spin connection sectors.

Findings

The action is Dirac-consistent and first class.

It connects different formulations of general relativity.

Provides a method to transform between related sectors.

Abstract

In this paper we provide an action related to a certain sector of general relativity where the algebra of Hamiltonian constraints forms a first class system. This action is a Dirac-consistent stand-alone action with two physical degrees of freedom per point. In this paper we provide the steps necessary to transform this new action to and from the associated sectors of the Ashtekar theory and a certain antecedent of the pure spin connection formulation by Capovilla, Dell and Jacobson.