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arXiv quant-ph/02080552002-08quant-ph

Generalized (s-Parameterized) Weyl Transformation

Alex Granik

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

英文摘要：

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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