Hamiltonian embedding of the massive Yang-Mills theory and the generalized St\"uckelberg formalism

TL;DR

This paper develops a gauge-invariant Hamiltonian formulation of the massive Yang-Mills theory by embedding it into an extended phase space, explicitly computing correction terms, and linking extra fields to the St"uckelberg formalism.

Contribution

It introduces a Hamiltonian embedding method for the massive Yang-Mills theory, explicitly deriving correction terms and connecting auxiliary fields to the St"uckelberg approach.

Findings

Explicit correction terms for gauge invariance are derived.

Extra fields correspond to St"uckelberg scalars.

The formulation ensures involutive constraints and Hamiltonian.

Abstract

Using the general notions of Batalin, Fradkin, Fradkina and Tyutin to convert second class systems into first class ones, we present a gauge invariant formulation of the massive Yang-Mills theory by embedding it in an extended phase space. The infinite set of correction terms necessary for obtaining the involutive constraints and Hamiltonian is explicitly computed and expressed in a closed form. It is also shown that the extra fields introduced in the correction terms are exactly identified with the auxiliary scalars used in the generalized St\"uckelberg formalism for converting a gauge noninvariant Lagrangian into a gauge invariant form.