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.
Applications of the Weyl-Wigner formalism to noncommutative geometry,
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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.