Injective tensor products in strict deformation quantization
Simone Murro, Christiaan J. F. van de Ven
TL;DR
This paper establishes criteria for strict deformation quantization of tensor products of Poisson algebras, explores KMS state products, and links quantum and classical Hamiltonians in spin systems with applications to many-particle Schrödinger operators.
Contribution
It provides necessary and sufficient conditions for tensor product quantizations and analyzes the existence of KMS state products, connecting quantum and classical Hamiltonians.
Findings
Criteria for strict deformation quantization of tensor products
Conditions for the existence of KMS state products
Relation between Schrödinger resolvent and quantization maps
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra