Inequivalent Vacuum States in Algebraic Quantum Theory

TL;DR

This paper explores the GNS representation in topological involutive algebras for quantum systems, showing that inequivalent states can be viewed as classical fields similar to a Higgs vacuum.

Contribution

It generalizes the GNS construction to broader algebraic frameworks and interprets inequivalent states as classical fields, providing new physical insights.

Findings

Characterization of inequivalent state spaces

Representation of inequivalent states as classical fields

Analogy with Higgs vacuum field

Abstract

The GNS representation construction is considered in a general case of topological involutive algebras of quantum systems, including quantum fields, and inequivalent state spaces of these systems are characterized. We aim to show that, from the physical viewpoint, they can be treated as classical fields by analogy with a Higgs vacuum field.