Differential operators on supercircle: conformally equivariant quantization and symbol calculus

Hichem Gargoubi; Najla Mellouli; Valentin Ovsienko

doi:10.1007/s11005-006-0129-8

Differential operators on supercircle: conformally equivariant quantization and symbol calculus

数学物理 2015-06-26 v2 math.MP 表示论

作者: Hichem Gargoubi , Najla Mellouli , Valentin Ovsienko

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摘要

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.

关键词

operator theory and quantum mechanics lie algebras and representations

引用

@article{arxiv.math-ph/0610059,
  title  = {Differential operators on supercircle: conformally equivariant quantization and symbol calculus},
  author = {Hichem Gargoubi and Najla Mellouli and Valentin Ovsienko},
  journal= {arXiv preprint arXiv:math-ph/0610059},
  year   = {2015}
}

Differential operators on supercircle: conformally equivariant quantization and symbol calculus

摘要

关键词

引用

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