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 Poincaré disc.

25 pages. Awarded with the Prix du Concour annuel 2018: On demande une contribution à la construction d'un cadre convergent pour la quantification par déformation of the Académie royale des Sciences, des Lettres et des Beaux-Arts de Belgique

References in corpus (3)

• The deformation quantizations of the hyperbolic plane
• Poisson geometry and Morita equivalence
• Quantization of Kähler manifolds

Cited by in corpus (1)

• Group Actions in Deformation Quantisation