Categorical Perspective on Quantization of Poisson Algebra
| Autor: | Akifumi Sako, Jumpei Gohara, Yuji Hirota |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
High Energy Physics - Theory
Mathematics - Differential Geometry Generalization Structure (category theory) FOS: Physical sciences Poisson distribution 01 natural sciences symbols.namesake Perspective (geometry) Mathematics::Category Theory 0103 physical sciences FOS: Mathematics 0101 mathematics Categorical variable Mathematical Physics Poisson algebra Mathematics Quantization (signal processing) 010102 general mathematics Statistical and Nonlinear Physics Mathematical Physics (math-ph) Algebra High Energy Physics - Theory (hep-th) Differential Geometry (math.DG) symbols 010307 mathematical physics Matrix regularization |
| DOI: | 10.48550/arxiv.1907.08665 |
| Popis: | We propose a generalization of quantization as a categorical way. For a fixed Poisson algebra quantization categories are defined as subcategories of R-module category with the structure of classical limits. We construct the generalized quantization categories including matrix regularization, strict deformation quantization, prequantization, and Poisson enveloping algebra, respectively. It is shown that the categories of strict deformation quantization, prequantization, and matrix regularization with some conditions are categorical equivalence. On the other hand, the categories of Poisson enveloping algebra is not equivalent to the other categories. Comment: 20 pages; In v3, some inaccuracies are corrected and preconditions in propositions 2.5, 7.1, 7.2, 7.3, and 7.7 are added. Definitions and theorems in section 5 are revised. Theorem 4.6 is added. Appendix A and B are added. v3 has minor changes in definition 3.1 and 4.1 |
| Databáze: | OpenAIRE |
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