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Quantum Mechanics in Phase Space
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Ever since Werner Heisenberg's 1927 paper on uncertainty, there has been considerable hesitancy in simultaneously considering positions and momenta in quantum contexts, since these are incompatible observables. But this persistent discomfort with addressing positions and momenta jointly in the quantum world is not really warranted, as was first fully appreciated by Hilbrand Groenewold and Jos\'e Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that time, it was not completely understood nor widely known --- much less generally accepted --- until the late 20th century.
Forward citations
Cited by 3 Pith papers
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Complex Weyl correspondence for a generalized diamond group
The complex Weyl correspondence is shown to be a Stratonovich-Weyl correspondence for the generic representations of the generalized diamond group, with explicit Berezin and Weyl symbols.
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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.
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Hall conductivity as the topological invariant in phase space in the presence of interactions and non-uniform magnetic field
Interactions do not renormalize the phase-space topological expression for the Hall conductivity in a 2+1D tight-binding model with non-uniform magnetic field, to all orders of perturbation theory.
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