A pure Dirac's canonical analysis for four-dimensional BF theories

TL;DR

This paper conducts a detailed Dirac's canonical analysis of four-dimensional BF theories, identifying symmetries, constraints, and degrees of freedom, and compares these findings with existing literature.

Contribution

It provides a pure Dirac's canonical framework for 4D BF theories, clarifying their symmetries and constraints without auxiliary assumptions.

Findings

Identified the complete set of constraints and symmetries.

Determined the physical degrees of freedom in the theories.

Compared results with alternative approaches in literature.

Abstract

We perform Dirac's canonical analysis for a four-dimensional $BF$ and for a generalized four-dimensional $BF$ theory depending on a connection valued in the Lie algebra of SO(3,1). This analysis is developed by considering the corresponding complete set of variables that define these theories as dynamical, and we find out the relevant symmetries, the constraints, the extended Hamiltonian, the extended action, gauge transformations and the counting of physical degrees of freedom. The results obtained are compared with other approaches found in the literature.