On the mixing property for a class of states of relativistic quantum fields

TL;DR

This paper proves the existence of space and time translation invariant states close to a given relativistic quantum field state, with the property that their time evolution becomes asymptotically abelian, under certain regularity conditions.

Contribution

It establishes the mixing property for a class of states of relativistic quantum fields, including ground and thermal states, showing their asymptotic abelian behavior.

Findings

Existence of translation invariant states close to the original state.

Time evolution of these states is weakly asymptotically abelian.

Applicable to ground and thermal states of relativistic quantum fields.

Abstract

Let $\omega$ be a factor state on the quasi-local algebra $\cal{A}$ of observables generated by a relativistic quantum field, which in addition satisfies certain regularity conditions (satisfied by ground states and the recently constructed thermal states of the $P(\phi)_2$ theory). We prove that there exist space and time translation invariant states, some of which are arbitrarily close to $\omega$ in the weak* topology, for which the time evolution is weakly asymptotically abelian.