Connes' tangent groupoid and strict quantization

[摘要] We address one of the open problems in quantization theory recently listed by Rieffel. By developing in detail Comes' tangent groupoid principle and using previous work by Landsman, we show how to construct a strict flabby quantization, which is moreover an asymptotic morphism and satisfies the reality and traciality constraints, on any oriented Riemannian manifold. That construction generalizes the standard Moyal rule. The paper can be considered as an introduction to quantization theory from Connes' point of view. (C) 1999 Elsevier Science B.V. Subj. Class.: Quantum mechanics 1991 MSG: 32G08, 81S10, 46L87, 81S99.

[发布日期] 1999-12-01

[关键词] Connes' tangent groupoid;deformation quantization