Categorical perspective on quantization of Poisson algebra

We propose a generalization of quantization using a categorical approach. For a fixed Poisson algebra, quantization categories are defined as subcategories of the R-module category equipped with the structure of classical limits. We then construct the generalized quantization categories including ma...

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Bibliographic Details
Published inJournal of mathematical physics Vol. 61; no. 7
Main Authors Gohara, Jumpei, Hirota, Yuji, Sako, Akifumi
Format Journal Article
LanguageEnglish
Published 01.07.2020
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Summary:We propose a generalization of quantization using a categorical approach. For a fixed Poisson algebra, quantization categories are defined as subcategories of the R-module category equipped with the structure of classical limits. We then construct the generalized quantization categories including matrix regularization, strict deformation quantization, prequantization, and Poisson enveloping algebra. It is shown that the categories of strict deformation quantization, prequantization, and matrix regularization with certain conditions are equivalent categories. On the other hand, the categories of Poisson enveloping algebra are not equivalent to the other categories.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5145262