Convergence of Star Product: From Examples to a General Framework
Abstract
We recall some of the fundamental achievements of formal deformation quantization to argue that one of the most important remaining problems is the question of convergence. Here we discuss different approaches found in the literature so far. The recent developments of finding convergence conditions are then outlined in three basic examples: the Weyl star product for constant Poisson structures, the Gutt star product for linear Poisson structures, and the Wick type star product on the Poincar\'e disc.
Keywords
Cite
@article{arxiv.1901.11327,
title = {Convergence of Star Product: From Examples to a General Framework},
author = {Stefan Waldmann},
journal= {arXiv preprint arXiv:1901.11327},
year = {2019}
}
Comments
25 pages. Awarded with the Prix du Concour annuel 2018: On demande une contribution \`a la construction d'un cadre convergent pour la quantification par d\'eformation of the Acad\'emie royale des Sciences, des Lettres et des Beaux-Arts de Belgique