Quantized Kronecker flows and almost periodic quantum field theory

We define and study the properties of the infinite dimensional quantized Kronecker flow. This ${\text{bC}}^{\ast }$-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 ${\text{bC}}^{\ast }$-algebras of observables arising in these theories.