The Abelian Embedding Formulation of the Stueckelberg Model and its Power-counting Renormalizable Extension

TL;DR

This paper presents a geometric and algebraic reformulation of the non-abelian Stueckelberg model using BRST techniques, introduces a power-counting renormalizable extension, and confirms the physical spectrum includes a massive scalar.

Contribution

It introduces an abelian embedding formulation with BRST techniques for the non-abelian Stueckelberg model and constructs a power-counting renormalizable extension.

Findings

Existence of a natural off-shell nilpotent BRST differential

Construction of a power-counting renormalizable extension

Physical spectrum includes a massive scalar particle

Abstract

We elucidate the geometry of the polynomial formulation of the non-abelian Stueckelberg mechanism. We show that a natural off-shell nilpotent BRST differential exists allowing to implement the constraint on the sigma field by means of BRST techniques. This is achieved by extending the ghost sector by an additional U(1) factor (abelian embedding). An important consequence is that a further BRST-invariant but not gauge-invariant mass term can be written for the non-abelian gauge fields. As all versions of the Stueckelberg theory, also the abelian embedding formulation yields a non power-counting renormalizable theory in D=4. We then derive its natural power-counting renormalizable extension and show that the physical spectrum contains a physical massive scalar particle. Physical unitarity is also established. This model implements the spontaneous symmetry breaking in the abelian embedding formalism.