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Generalized (s-Parameterized) Weyl Transformation

Alex Granik
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Abstract

A general canonical transformation of mechanical operators of position and momentum is considered. It is shown that it automatically generates a parameter s which leads to a generalized (or s-parameterized) Wigner function. This allows one to derive a generalized (s-parameterized) Moyal brackets for any dimensions. In the classical limit the s-parameterized Wigner averages of the momentum and its square yield the respective classical values. Interestingly enough,in the latter case the classical Hamilton-Jacobi equation emerges as a consequence of such a transition only if there is a non-zero parameter s.

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Alex Granik. 2003-11-11. Generalized (s-Parameterized) Weyl Transformation. https://arxiv.org/abs/quant-ph/0208055

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