Polysymplectic formulation for topologically massive Yang–Mills field theory

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 [Formula: see text]-forms in order to obtain the correct field equations, in opposition to certain examples found in the literature.