Duality symmetry for star products
arXiv:hep-th/0407131 · doi:10.1016/j.physleta.2004.11.027
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.
14 pages, no figures