General massive gauge theory

TL;DR

This paper constructs massive gauge theories using perturbative gauge invariance, deriving the structure of interactions and scalar fields, culminating in the unique emergence of the electroweak theory with specific gauge groups.

Contribution

It provides a systematic derivation of massive gauge theories and the electroweak model solely from gauge invariance principles without assuming spontaneous symmetry breaking.

Findings

Derivation of gauge interactions including Goldstone and Higgs bosons

Unique emergence of the electroweak $SU(2)\times U(1)$ model

Determination of couplings and potentials from gauge invariance

Abstract

The concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is used to construct massive gauge theories. We consider the interactions of $r$ massive and $s$ massless gauge fields together with $(r+s)$ fermionic ghost and anti-ghost fields. First order gauge invariance requires the introduction of unphysical scalars (Goldstone bosons) and fixes their trilinear couplings. At second order additional physical scalars (Higgs fields) are necessary, their coupling is further restricted at third order. In case of one physical scalar all couplings are determined by gauge invariance, including the Higgs potential. For three massive and one massless gauge field the $SU(2)\times U(1)$ electroweak theory comes out as the unique solution.