Injective Tensor Products in Strict Deformation Quantization

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2021-12-24 DOI:10.1007/s11040-021-09414-1

Simone Murro, Christiaan J. F. van de Ven

引用次数: 5

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.

查看原文本刊更多论文

严格变形量化中的内射张量积

本文的目的是双重的。首先给出了泊松代数张量积严格变形量化存在的充分必要判据，然后讨论了KMS态积的存在性。作为应用，我们讨论了自旋系统中量子哈密顿量与经典哈密顿量的对应关系，并给出了非相互作用多粒子系统中Schödinger算子的解与量子化映射之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.