A sharpened nuclearity condition and the uniqueness of the vacuum in QFT

TL;DR

This paper introduces a new phase space condition in quantum field theory that ensures the uniqueness of the vacuum state, demonstrating its validity in free field models and analyzing local operator momentum transfer.

Contribution

It proposes a novel phase space criterion related to energy additivity, establishing vacuum uniqueness in QFT under this condition and verifying it in free field theory.

Findings

Uniqueness of vacuum under the new phase space condition

Verification of the condition in massive free field theory

Detailed analysis of local operator momentum transfer

Abstract

It is shown that only one vacuum state can be prepared with a finite amount of energy and it appears, in particular, as a limit of physical states under large timelike translations in any theory which satisfies a phase space condition proposed in this work. This new criterion, related to the concept of additivity of energy over isolated subsystems, is verified in massive free field theory. The analysis entails very detailed results about the momentum transfer of local operators in this model.