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 \(sl(m+1,\mathbb{R})\)-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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Mathematics Subject Classification (2000). 53B05, 53B10, 53D50, 53C10
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Mathonet, P., Radoux, F. Natural and Projectively Equivariant Quantizations by means of Cartan Connections. Lett Math Phys 72, 183–196 (2005). https://doi.org/10.1007/s11005-005-6783-4
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DOI: https://doi.org/10.1007/s11005-005-6783-4