Injective tensor products in strict deformation quantization
Mathematical Physics
2022-02-24 v3 Functional Analysis
math.MP
Operator Algebras
Quantum Algebra
Abstract
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 Sch\"odinger operators for non-interacting many-particle systems and quantization maps.
Cite
@article{arxiv.2010.03469,
title = {Injective tensor products in strict deformation quantization},
author = {Simone Murro and Christiaan J. F. van de Ven},
journal= {arXiv preprint arXiv:2010.03469},
year = {2022}
}
Comments
16 pages -- accepted in Mathematical Physics, Analysis and Geometry