Projectively Equivariant Quantization Map

Details Projectively Equivariant Quantization Map Projectively Equivariant Quantization Map

2000-03-09

arxiv.org/abs/math/0003054v2

Lett. Math. Phys. 51 (4), 2000

Mathematics

Differential Geometry

The results of this paper have been surpassed by several results. The title has been corrected to avoid wrong citations

Scientific paper

Let M be a manifold endowed with a symmetric affine connection $\Gamma.$ The aim of this paper is to describe a quantization map between the space of second-order polynomials on the cotangent bundle T^{*} M and the space of second-order linear differential operators, both viewed as modules over the group of diffeomorphisms and the Lie algebra of vector fields on M. This map is an isomorphism, for almost all values of certain constants, and it depend only on the projective class of the affine connection $\Gamma.$

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