Extended covariance under nonlinear canonical transformation in Weyl quantization

Details Extended covariance under nonlinear canonical transformation in Weyl quantization Extended covariance under nonlinear canonical transformation in Weyl quantization

2000-11-18

arxiv.org/abs/quant-ph/0011076v3

Physics

Quantum Physics

21 pages, no figures

Scientific paper

A theory of nonunitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. Exact solutions of the transformation kernels and the phase space propagators are given for the three fundamental canonical maps as fractional-linear, gauge and contact (point) transformations. Under the nonlinear maps a phase space representation is mapped to another phase space representation thereby extending the standard concept of covariance. This extended covariance allows Dirac-Jordan transformation theory to naturally emerge from the Hilbert space representations in the Weyl quantization.

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