80 research outputs found
Conformally equivariant quantization: Existence and uniqueness
We prove the existence and the uniqueness of a conformally equivariant symbol
calculus and quantization on any conformally flat pseudo-Riemannian manifold
(M,\rg). In other words, we establish a canonical isomorphism between the
spaces of polynomials on and of differential operators on tensor
densities over , both viewed as modules over the Lie algebra \so(p+1,q+1)
where . This quantization exists for generic values of the weights
of the tensor densities and compute the critical values of the weights yielding
obstructions to the existence of such an isomorphism. In the particular case of
half-densities, we obtain a conformally invariant star-product.Comment: LaTeX document, 32 pages; improved versio
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