Manifestly Lorentz-covariant variables for the phase space of general relativity

TL;DR

This paper introduces a Lorentz-covariant phase space formulation for general relativity with the Immirzi parameter, providing new variables that generalize Barbero's formulation and preserve Lorentz covariance.

Contribution

It presents a manifestly Lorentz-covariant set of phase space variables for general relativity, extending previous formulations and clarifying the structure of constraints.

Findings

New Lorentz-covariant variables for the phase space

Canonical transformations relate different Lorentz-covariant parametrizations

In the time gauge, variables reduce to Barbero's formulation

Abstract

We present a manifestly Lorentz-covariant description of the phase space of general relativity with the Immirzi parameter. This formulation emerges after solving the second-class constraints arising in the canonical analysis of the Holst action. We show that the new canonical variables give rise to other Lorentz-covariant parametrizations of the phase space via canonical transformations. The resulting form of the first-class constraints in terms of new variables is given. In the time gauge, these variables and the constraints become those found by Barbero.