Paper detail

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

Let $ω$ 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 $P(ϕ)_2$ theory). We prove that there exist space and time translation invariant states, some of which are arbitrarily close to $ω$ in the weak* topology, for which the time evolution is weakly asymptotically abelian.