On the Semi-Classical Vacuum Structure of the Electroweak Interaction

TL;DR

This paper explores the semi-classical vacuum structure of the electroweak interaction, linking the moduli space of vacua to topological properties of space-time and implications for gauge bundles and the Aharonov-Bohm effect.

Contribution

It provides a novel interpretation of the electroweak vacuum moduli space using de Rham cohomology and relates the triviality of gauge bundles to the Higgs ground state and electromagnetic interactions.

Findings

Vacua moduli space identified with first de Rham cohomology group.

Existence of Higgs ground state linked to triviality of the electroweak gauge bundle.

Implications for quantization of electromagnetism on curved space-time.

Abstract

It is shown that in the semi-classical approximation of the electroweak sector of the Standard Model the moduli space of vacua can be identified with the first de Rham cohomology group of space-time. This gives a slightly different physical interpretation of the occurrence of the well-known Ahoronov-Bohm effect. Moreover, when charge conjugation is taken into account, the existence of a non-trivial ground state of the Higgs boson is shown to be equivalent to the triviality of the electroweak gauge bundle. As a consequence, the gauge bundle of the electromagnetic interaction must also be trivial. Though derived at ``tree level'' the results presented here may also have some consequences for quantizing, e. g., electromagnetism on an arbitrary curved space-time.