Canonical analysis of $BF$ gravity in $n$ dimensions

TL;DR

This paper performs a covariant canonical analysis of $BF$ gravity in arbitrary dimensions, demonstrating that the Hamiltonian formulation aligns with previous results from the Palatini action without introducing second-class constraints.

Contribution

It provides a manifestly covariant canonical analysis of $BF$ gravity in $n$ dimensions, showing equivalence with known formulations and avoiding second-class constraints.

Findings

Canonical analysis achieved without second-class constraints

Hamiltonian formulation matches previous Palatini-based results

Analysis performed in both $SO(n-1,1)$ and $SO(n)$ covariant forms

Abstract

In this paper we perform in a manifestly $SO(n-1,1)$ [or, alternatively $SO(n)$] covariant fashion, the canonical analysis of general relativity in $n$ dimensions written as a constrained $BF$ theory. Since the Lagrangian action of the theory can be written in two classically equivalent ways, we analyze each case separately. We show that for either action the canonical analysis can be accomplished without introducing second-class constraints during the whole process. Furthermore, in each case the resulting Hamiltonian formulation is the same as the canonical formulation with only first-class constraints recently obtained in M. Montesinos, R. Escobedo, J. Romero, and M. Celada, Phys. Rev. D 101, 024042 (2020) from the $n$-dimensional Palatini action.