Abstract
An explicit expression of the “Wigner operator” is derived, such that the Wigner function of a quantum state is equal to the expectation value of this operator with respect to the same state. This Wigner operator leads to a representation-independent procedure for establishing the correspondence between the inhomogeneous symplectic group applicable to linear canonical transformations in classical mechanics and the Weyl-metaplectic group governing the symmetry of unitary transformations in quantum mechanics.
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Yeh, L., Kim, Y.S. Correspondence between the classical and quantum canonical transformation groups from an operator formulation of the wigner function. Found Phys 24, 873–884 (1994). https://doi.org/10.1007/BF02067652
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DOI: https://doi.org/10.1007/BF02067652