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arXiv · hep-th/0407131

Duality symmetry for star products

V. I. Man'ko·G. Marmo·P. Vitale
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Abstract

A duality property for star products is exhibited. In view of it, known star-product schemes, like the Weyl-Wigner-Moyal formalism, the Husimi and the Glauber-Sudarshan maps are revisited and their dual partners elucidated. The tomographic map, which has been recently described as yet another star product scheme, is considered. It yields a noncommutative algebra of operator symbols which are positive definite probability distributions. Through the duality symmetry a new noncommutative algebra of operator symbols is found, equipped with a new star product. The kernel of the new star product is established in explicit form and examples are considered.

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V. I. Man'ko, G. Marmo, P. Vitale. 2004-07-15. Duality symmetry for star products. https://doi.org/10.1016/j.physleta.2004.11.027

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