# Polysymplectic formulation for topologically massive Yang-Mills field theory

## TL;DR

This paper develops a covariant polysymplectic formulation for topologically massive Yang-Mills theory, providing a new approach to derive field equations without the usual constraint analysis.

## Contribution

It introduces a method to obtain regular Lagrangians from singular ones using polymomenta, simplifying the derivation of covariant field equations.

## Key findings

- Successfully derived covariant De Donder-Weyl equations for the theory.
- Avoided standard constraint analysis by choosing appropriate polymomenta.
- Highlighted the importance of $(n-1)$-forms in obtaining correct field equations.

## Abstract

We analyze the De Donder-Weyl covariant field equations for the topologically massive Yang-Mills theory. These equations are obtained through the Poisson-Gerstenhaber bracket described within the polysymplectic framework. Even though the Lagrangian defining the system of our interest is singular, we show that by appropriately choosing the polymomenta one may obtain an equivalent regular Lagrangian, thus avoiding the standard analysis of constraints. Further, our simple treatment allows us to only consider the privileged $(n-1)$-forms in order to obtain the correct field equations, in opposition to certain examples found in the literature.