Associative algebras, punctured disks and the quantization of Poisson manifolds
Quantum Algebra
2013-09-30 v2 High Energy Physics - Theory
Abstract
The aim of the note is to provide an introduction to the algebraic, geometric and quantum field theoretic ideas that lie behind the Kontsevich-Cattaneo-Felder formula for the quantization of Poisson structures. We show how the quantization formula itself naturally arises when one imposes the following two requirements to a Feynman integral: on the one side it has to reproduce the given Poisson structure as the first order term of its perturbative expansion; on the other side its three-point functions should describe an associative algebra. It is further shown how the Magri-Koszul brackets on 1-forms naturally fits into the theory of the Poisson sigma-model.
Keywords
Cite
@article{arxiv.math/0309320,
title = {Associative algebras, punctured disks and the quantization of Poisson manifolds},
author = {Domenico Fiorenza and Riccardo Longoni},
journal= {arXiv preprint arXiv:math/0309320},
year = {2013}
}
Comments
LaTeX, 8 pages, uses XY-pic. Few typos corrected. Final version