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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical physics 2020-07, Vol.61 (7)
Main Authors: Gohara, Jumpei, Hirota, Yuji, Sako, Akifumi
Format: Article
Language:English
Subjects:
Algebra
Categories
Deformation
Equivalence
Measurement
Physics
Regularization
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
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