A pure Dirac's method for Yang-Mills expressed as a constrained BF-like theory

TL;DR

This paper applies a pure Dirac's method to a constrained BF-like formulation of Yang-Mills theory, analyzing its phase space, constraints, and gauge structure to establish classical equivalence and discuss quantization.

Contribution

It introduces a comprehensive Dirac's analysis of a BF-like formulation of Yang-Mills, detailing the constraint structure and gauge symmetries, and compares it with existing models.

Findings

The BF-like theory is classically equivalent to Yang-Mills.

The complete phase space analysis reveals the constraint algebra.

Discussion on potential quantization approaches.

Abstract

A pure Dirac's method of Yang-Mills expressed as a constrained BF-like theory is performed. In this paper we study an action principle composed by the coupling of two topological BF-like theories, which at the Lagrangian level reproduces Yang-Mills equations. By a pure Dirac's method we mean that we consider all the variables that occur in the Lagrangian density as dynamical variables and not only those ones that involve temporal derivatives. The analysis in the complete phase space enable us to calculate the extended Hamiltonian, the extended action, the constraint algebra, the gauge transformations and then we carry out the counting of degrees of freedom. We show that the constrained BF-like theory correspond at classical level to Yang-Mills theory. From the results obtained, we discuss briefly the quantization of the theory. In addition we compare our results with alternatives models that have been reported in the literature