Hamiltonian analysis for topological and Yang-Mills theories expressed as a constrained BF-like theory

TL;DR

This paper performs a Hamiltonian analysis of topological invariants and BF-like theories, revealing differences in their symplectic structures and implications for quantum formulations, with applications to Yang-Mills theories.

Contribution

It provides a detailed Hamiltonian analysis of Euler and Second-Chern classes, highlighting differences in symplectic structures despite similar equations of motion, and explores symmetries in BF-like formulations of Yang-Mills theories.

Findings

Different symplectic structures for Euler and Second-Chern classes.

Identified symmetries leading to Yang-Mills equations.

Implications for quantum formulations of topological theories.

Abstract

The Hamiltonian analysis for the Euler and Second-Chern classes is performed. We show that, in spite of the fact that the Second-Chern and Euler invariants give rise to the same equations of motion, their corresponding symplectic structures on the phase space are different, therefore, one can expect different quantum formulations. In addition, the symmetries of actions written as a BF-like theory that lead to Yang-Mills equations of motion are studied. A close relationship with the results obtained in previous works for the Second-Chern and Euler classes is found.