Connes' Tangent Groupoid and Strict Quantization

Details Connes' Tangent Groupoid and Strict Quantization Connes' Tangent Groupoid and Strict Quantization

1998-02-20

arxiv.org/abs/math/9802102v3

Mathematics

Differential Geometry

LaTeX file, 22 pages (elsart.cls required). Minor changes. Final version to appear in J. Geom. and Phys

Scientific paper

10.1016/S0393-0440(98)00028-X

We address one of the open problems in quantization theory recently listed by Rieffel. By developping in detail Connes' 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.

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