Strict deformation quantization in locally interacting quantum spin models

Abstract

Quantization in general refers to the transition from a classical to a corresponding quantum theory. The inverse issue, called the classical limit of quantum theories, is considered a much more difficult problem. A rigorous and natural framework that addresses this problem exists under the name strict (or C*-algebraic) deformation quantization. In this talk, I will first introduce this concept by means of relevant definitions. I will then show how this framework can be applied in studying the macroscopic limit of lattice quantum spin systems, starting with a brief summary of mean-field quantum theories. Finally, I will discuss the results of a recent work and show how strict deformation quantization applies to more realistic models described by local interaction quantum spin models, e.g. the quantum Heisenberg spin chain.