Abstract
The aim of this paper is twofold. 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.
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Acknowledgements
We are grateful to Federico Bambozzi, Francesco Fidaleo, Klaas Landsman, Valter Moretti and Teun van Nuland for helpful discussions related to the topic of this paper. We are grateful to the referee for the useful comments.
Funding
S.M is supported by the the DFG research Grant MU 4559/1-1 “Hadamard States in Linearized Quantum Gravity” and thanks the support of the INFN-TIFPA project “Bell” and the University of Trento during the initial stages of this project. The second author is funded by the ‘INdAM Doctoral Programme in Mathematics and/or Applications’ co-funded by Marie Sklodowska–Curie Actions, INdAM-DPCOFUND-2015, Grant Number 713485.
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Murro, S., van de Ven, C.J.F. Injective Tensor Products in Strict Deformation Quantization. Math Phys Anal Geom 25, 2 (2022). https://doi.org/10.1007/s11040-021-09414-1
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DOI: https://doi.org/10.1007/s11040-021-09414-1
Keywords
- Strict deformation quantization
- Injective tensor product
- Minimal \(C^*\)-norm
- Resolvent algebras
- Quantum spin system
- Heisenberg model
- Ising model
- Curie–Weiss model