Natural and projectively equivariant quantizations by means of Cartan Connections

Details Natural and projectively equivariant quantizations by means of Cartan Connections Natural and projectively equivariant quantizations by means of Cartan Connections

2006-06-22

arxiv.org/abs/math/0606554v1

Lett. Math. Phys., 72(3):183-196, 2005

Mathematics

Differential Geometry

13 pages

Scientific paper

The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of Thomas-Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivariant quantization if and only if an \sl(m+1,\R)-equivariant quantization exists in the flat situation in the sense of [18], thus solving one of the problems left open by M. Bordemann.

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