A Real Polynomial Formulation of General Relativity in terms of Connections

TL;DR

This paper introduces a new polynomial Hamiltonian formulation of Lorentzian General Relativity using two real $SO(3)$ connections, simplifying the constraints while retaining key features of Ashtekar's approach.

Contribution

It presents a novel real polynomial Hamiltonian formulation of General Relativity with simpler constraints, avoiding the complexities of the Ashtekar formulation.

Findings

Constraints are simple polynomials in basic variables

Framework retains key features of Ashtekar formulation

Provides a new real connection-based formulation of GR

Abstract

I show in this letter that it is possible to construct a Hamiltonian description for Lorentzian General Relativity in terms of two real $SO(3)$ connections. The constraints are simple polynomials in the basic variables. The present framework gives us a new formulation of General Relativity that keeps some of the interesting features of the Ashtekar formulation without the complications associated with the complex character of the latter.