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.
Complex Weyl symbols of metaplectic operators: an elementary approach
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abstract
We give explicit formulas for the Berezin symbols and the complex Weyl symbols of the metaplectic representation operators by using the holomorphic representations of the Jacobi group. Then we recover some known formulas for the symbols of the metaplectic operators in the classical Weyl calculus, in particular for the classical Weyl symbol of the exponential of an operator whose Weyl symbol is a quadratic form.
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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.