Connes' Tangent Groupoid and Strict Quantization

@article{Cariena1998ConnesTG,
  title={Connes' Tangent Groupoid and Strict Quantization},
  author={J. F. Cari{\~n}ena and J. Clemente-Gallardo and E. Follana and J. Gracia-Bond'ia and A. Rivero and J. C. V'arilly},
  journal={arXiv: Differential Geometry},
  year={1998}
}
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… Expand
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