Coincidence Arrangements of Local Observables and Uniqueness of the Vacuum in QFT

TL;DR

This paper introduces a new phase space criterion for local observables in quantum field theory, ensuring vacuum uniqueness and purity, and verifies it in free field models.

Contribution

It proposes a novel phase space condition that links local observable arrangements to vacuum properties, extending existing compactness criteria.

Findings

The new criterion is equivalent to a known compactness condition.

It is verified in massive free field theory.

Ensures uniqueness and purity of vacuum states.

Abstract

A new phase space criterion, encoding the physically motivated behavior of coincidence arrangements of local observables, is proposed in this work. This condition entails, in particular, uniqueness and purity of the energetically accessible vacuum states. It is shown that the qualitative part of this new criterion is equivalent to a compactness condition proposed in the literature. Its novel quantitative part is verified in massive free field theory.