General method for including Stueckelberg fields

TL;DR

This paper introduces a systematic, covariant method for incorporating Stueckelberg fields into Lagrangian theories using involutive closure, ensuring gauge invariance and stability of degrees of freedom.

Contribution

It develops an iterative procedure for constructing gauge-invariant actions with Stueckelberg fields based on involutive closure, extending the BV formalism.

Findings

Provides a covariant degree of freedom count method.

Proves existence of Stueckelberg-invariant actions.

Constructs gauge symmetry generators from closure operators.

Abstract

A systematic procedure is proposed for inclusion of Stueckelberg fields. The procedure begins with the involutive closure when the original Lagrangian equations are complemented by all the lower order consequences. The involutive closure can be viewed as Lagrangian analogue of complementing constrained Hamiltonian system with secondary constraints. The involutively closed form of the field equations allows for explicitly covariant degree of freedom number count, which is stable with respect to deformations. If the original Lagrangian equations are not involutive, the involutive closure will be a non-Lagrangian system. The Stueckelberg fields are assigned to all the consequences included into the involutive closure of the Lagrangian system. The iterative procedure is proposed for constructing the gauge invariant action functional involving Stueckelberg fields such that Lagrangian equations are equivalent to the involutive closure of the original theory. The generators of the Stueckelberg gauge symmetry begin with the operators generating the closure of original Lagrangian system. These operators are not assumed to be a generators of gauge symmetry of any part of the original action, nor are they supposed to form an on shell integrable distribution. With the most general closure generators, the consistent Stueckelberg gauge invariant theory is iteratively constructed, without obstructions at any stage. The Batalin-Vilkovisky form of inclusion the Stueckelberg fields is worked out and existence theorem for the Stueckelberg action is proven.