The Equivalence Theorem at work: manifestly gauge-invariant Abelian Higgs model physics

TL;DR

This paper uses an algebraic approach with extended BRST symmetry to reformulate the Abelian Higgs model in gauge-invariant terms, enabling manifestly gauge-invariant calculations and demonstrating its renormalizability despite an infinite vertex structure.

Contribution

It introduces a gauge-invariant reformulation of the Abelian Higgs model using the Equivalence Theorem and extended BRST symmetry, showing its renormalizability and enabling gauge-invariant computations.

Findings

Reformulation in terms of gauge-invariant variables

Proof of renormalizability despite infinite vertices

Explicit calculation of gauge-invariant scalar propagator

Abstract

We reconsider the Equivalence Theorem from an algebraic viewpoint, using an extended BRST symmetry. This version of the Equivalence Theorem is then used to reexpress the Abelian Higgs model action, originally written in terms of undesirable gauge variant field excitations, in terms of gauge-invariant, physical variables, corresponding to the Fr\"ohlich-Morchio-Strocchi composite operators in the original field formulation. Although the ensuing action encompasses an infinite number of vertices and appears to be nonrenormalizable from the powercounting viewpoint, it nevertheless is renormalizable, thanks to the hidden equivalence with the original model. Hence, manifestly gauge-invariant computations are possible. We present an explicit illustration in terms of the gauge-invariant scalar field, its Green's function and corresponding pole mass.