Under s-ordered quantization, a Gaussian maps to a valid quantum state for lambda <= (1+s)^{-1}, and for antinormal ordering s=-1 even the delta function becomes the vacuum state.
Duality symmetry for star products
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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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From classical probability densities to quantum states: quantization of Gaussians for arbitrary orderings
Under s-ordered quantization, a Gaussian maps to a valid quantum state for lambda <= (1+s)^{-1}, and for antinormal ordering s=-1 even the delta function becomes the vacuum state.