Injective tensor products in strict deformation quantization

Simone Murro, Christiaan J. F. van de Ven
October 07, 2020
The aim of this paper is two-fold. Firstly we provide necessary and sufficient criteria for the existence of a strict deformation quantization of algebraic tensor products of Poisson algebras, and secondly, we discuss the existence of products of KMS states. As an application, we discuss the correspondence between quantum and classical Hamiltonians in spin systems and we provide a relation between the resolvent of Schödinger operators for non-interacting many-particle systems and quantization maps.

Strict deformation quantization, injective tensor product, minimal C ˚ -norm, resolvent algebras, quantum spin system, Heisenberg model, Ising model, Curie-Weiss model.