Injective tensor products in strict deformation quantization

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 Schödinger operators for non-interacting many-particle systems and quantization maps.

arXiv comment16 pages -- accepted in Mathematical Physics, Analysis and Geometry

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Cited by in corpus (4)

• The classical limit and spontaneous symmetry breaking in algebraic quantum theory
• DLR-KMS correspondence on lattice spin systems
• Classical and quantum KMS states on spin lattice systems
• Strict deformation quantization and local spin interactions