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Natural and projectively equivariant quantizations by means of Cartan Connections

P. Mathonet·F. Radoux
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Abstract

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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P. Mathonet, F. Radoux. 2006-06-22. Natural and projectively equivariant quantizations by means of Cartan Connections. https://doi.org/10.1007/s11005-005-6783-4

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