Deformation Quantization and Reduction
Quantum Algebra
2020-05-29 v2 High Energy Physics - Theory
Symplectic Geometry
Abstract
This note is an overview of the Poisson sigma model (PSM) and its applications in deformation quantization. Reduction of coisotropic and pre-Poisson submanifolds, their appearance as branes of the PSM, quantization in terms of L-infinity and A-infinity algebras, and bimodule structures are recalled. As an application, an "almost" functorial quantization of Poisson maps is presented if no anomalies occur. This leads in principle to a novel approach for the quantization of Poisson-Lie groups.
Cite
@article{arxiv.math/0701378,
title = {Deformation Quantization and Reduction},
author = {Alberto S. Cattaneo},
journal= {arXiv preprint arXiv:math/0701378},
year = {2020}
}
Comments
23 pages, 3 figures; added references, corrected typos