Differential operators on supercircle: conformally equivariant quantization and symbol calculus

Details Differential operators on supercircle: conformally equivariant quantization and symbol calculus Differential operators on supercircle: conformally equivariant quantization and symbol calculus

2006-10-24

arxiv.org/abs/math-ph/0610059v2

Physics

Mathematical Physics

Scientific paper

We consider the supercircle $S^{1|1}$ equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on $S^{1|1}$ as the Lie superalgebra of contact vector fields; it contains the M\"obius superalgebra $osp(1|2)$. We study the space of linear differential operators on weighted densities as a module over $osp(1|2)$. We introduce the canonical isomorphism between this space and the corresponding space of symbols and find interesting resonant cases where such an isomorphism does not exist.

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