Canonical analysis with no second-class constraints of $BF$ gravity with Immirzi parameter

TL;DR

This paper presents a Lorentz-covariant canonical analysis of $BF$ gravity with the Immirzi parameter, avoiding second-class constraints and connecting to recent first-order general relativity phase space formulations.

Contribution

It introduces a method to analyze $BF$ gravity canonically without second-class constraints, maintaining Lorentz covariance throughout.

Findings

Achieves Lorentz-covariant canonical analysis of $BF$ gravity

Avoids second-class constraints in the process

Connects to recent first-order gravity phase space descriptions

Abstract

In this paper we revisit the canonical analysis of $BF$ gravity with the Immirzi parameter and a cosmological constant. By examining the constraint on the $B$ field, we realize that the analysis can be performed in a Lorentz-covariant fashion while utterly avoiding the introduction of second-class constraints during the whole process. Finally, we make contact with the description of the phase space of first-order general relativity in terms of canonical variables with manifest Lorentz covariance subject to first-class constraints only recently introduced.