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Methods of Equivariant Quantization

C. Duval·P. Lecomte·V. Ovsienko
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Abstract

This article is a survey of recent work of the authors developing a new approach to quantization based on the equivariance with respect to some Lie group of symmetries. Examples are provided by conformal and projective differential geometry: given a smooth manifold M endowed with a flat conformal/projective structure, we establish a canonical isomorphism between the space of symmetric contravariant tensor fields on M and the space of differential operators on M. This leads to a notion of conformally/projectively invariant star-product on $T^*M$.

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C. Duval, P. Lecomte, V. Ovsienko. 1999-10-20. Methods of Equivariant Quantization. https://arxiv.org/abs/math/9910094

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