Local Normality for KMS states with Galilei invariant Interaction

TL;DR

This paper proves that KMS states for Galilei invariant Fermi systems with certain interactions are locally normal, and this property persists in the limit under specific conditions, linking modular automorphisms to time evolution.

Contribution

It establishes local normality of KMS states for Galilei invariant Fermi systems with cut-off interactions and extends this to the limit without cut-off under certain interaction conditions.

Findings

KMS states are locally normal with respect to Fock-space representation.

Local normality persists in the limit for repulsive or positive type interactions.

Modular automorphism coincides with the time evolution for the limit state.

Abstract

For Fermi systems interacting with a Galilei invariant pair potential with a cut-off for particles with highly different velocities the time evolution corresponds to an automorphism. We prove that all states satisfying the KMS-condition are locally normal with respect to the representation in Fock-space. Removing the cut-off limit states remain locally normal provided the interaction is repulsive or of positive type. The modular automorphism of the von Neumann-algebra of the limit state coincides with the time evolution.