Straightforward Hamiltonian analysis of $BF$ gravity in $n$ dimensions

TL;DR

This paper presents a Hamiltonian analysis of $BF$ gravity in arbitrary dimensions, maintaining covariance and avoiding explicit vielbein use, leading to a simplified first-class constraint formulation.

Contribution

It introduces a covariant Hamiltonian framework for $BF$ gravity in $n$ dimensions that naturally incorporates spacetime foliation without vielbein dependence.

Findings

Derived a covariant Hamiltonian formulation of $BF$ gravity in arbitrary dimensions.

Solved the $B$ field constraint in a foliation-adapted manner.

Obtained a Hamiltonian form with only first-class constraints.

Abstract

We perform, in a manifestly $SO(n-1,1)$ [$SO(n)$] covariant fashion, the Hamiltonian analysis of general relativity in $n$ dimensions written as a constrained $BF$ theory. We solve the constraint on the $B$ field in a way naturally adapted to the foliation of the spacetime that avoids explicitly the introduction of the vielbein. This leads to a form of the action involving a presymplectic structure, which is reduced by doing a suitable parametrization of the connection and then, after integrating out some auxiliary fields, the Hamiltonian form involving only first-class constraints is obtained.