Abstract
Let (M, g) be a pseudo-Riemannian manifold and \(\mathcal{F}_{\lambda } (M)\) the space of densities of degree λ on M. Denote \(\mathcal{D}_{{\lambda ,}\mu }^k (M)\) the space of differential operators from \(\mathcal{F}_{\lambda } (M)\) to \(\mathcal{F}_\mu (M)\) of order k and S δ k with δ = μ − λ the corresponding space of symbols. We construct (the unique) conformally invariant quantization map \(Q_{{\lambda ,}\mu }^3 :S_\delta ^3 \to \mathcal{D}_{{\lambda ,}\mu }^3 \). This result generalizes that of Duval and Ovsienko.
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Djounga, S.E.L. Conformally Invariant Quantization at Order Three. Letters in Mathematical Physics 64, 203–212 (2003). https://doi.org/10.1023/A:1025751120672
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DOI: https://doi.org/10.1023/A:1025751120672