Generalized (s-Parameterized) Weyl Transformation

Details Generalized (s-Parameterized) Weyl Transformation Generalized (s-Parameterized) Weyl Transformation

2002-08-08

arxiv.org/abs/quant-ph/0208055v3

Physics

Quantum Physics

LaTeX (amsmath, amsextra) 16 pages, appendix (fixing LaTex idiosincrasies); fixing some minor typos

Scientific paper

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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