Quantized Kronecker flows and almost periodic quantum field theory

TL;DR

This paper introduces the concept of quantized Kronecker flows as a new class of $C^*$-dynamical systems, explores their ergodic properties, and develops an almost periodic quantum field theory framework with unique equilibrium states.

Contribution

It defines and analyzes the properties of infinite dimensional quantized Kronecker flows and establishes existence and uniqueness of KMS states in related quantum field theories.

Findings

Proved an ergodic theorem for quantized Kronecker flows.

Established existence and uniqueness of KMS and super-KMS states.

Developed a framework for almost periodic quantum field theory.

Abstract

We define and study the properties of the infinite dimensional quantized Kronecker flow. This $\bC^*$-dynamical system arises as a quantization of the corresponding flow on an infinite dimensional torus. We prove an ergodic theorem for a class of quantized Kronecker flows. We also study the closely related almost periodic quantum field theory of bosonic, fermionic and supersymmetric particles. We prove the existence and uniqueness of KMS and super-KMS states for the $\bC^*$-algebras of observables arising in these theories.