BF Actions for the Husain-Kuchar Model

TL;DR

This paper reformulates the Husain-Kuchar model within BF theory, paving the way for its quantization using perturbative QFT or spin-foam methods, and explores the role of diffeomorphisms in these new formulations.

Contribution

It introduces a BF-theoretic formulation of the Husain-Kuchar model, facilitating its quantization via established quantum field theory techniques.

Findings

Husain-Kuchar model expressed as a BF theory.

Discussion of diffeomorphism roles in new formulations.

Potential for quantization using perturbative QFT or spin-foam approaches.

Abstract

We show that the Husain-Kuchar model can be described in the framework of BF theories. This is a first step towards its quantization by standard perturbative QFT techniques or the spin-foam formalism introduced in the space-time description of General Relativity and other diff-invariant theories. The actions that we will consider are similar to the ones describing the BF-Yang-Mills model and some mass generating mechanisms for gauge fields. We will also discuss the role of diffeomorphisms in the new formulations that we propose.