dorsal/arxiv
View SchemaExtended covariance under nonlinear canonical transformation in Weyl quantization
| Authors | T. Hakioglu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0011076 |
| URL | https://arxiv.org/abs/quant-ph/0011076 |
Abstract
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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"date_created": "2026-03-02T18:01:42.531000Z",
"date_modified": "2026-03-02T18:01:42.531000Z",
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"abstract": "A theory of nonunitary-invertible as well as unitary canonical\ntransformations is formulated in the context of Weyl\u0027s phase space\nrepresentations. Exact solutions of the transformation kernels and the phase\nspace propagators are given for the three fundamental canonical maps as\nfractional-linear, gauge and contact (point) transformations. Under the\nnonlinear maps a phase space representation is mapped to another phase space\nrepresentation thereby extending the standard concept of covariance. This\nextended covariance allows Dirac-Jordan transformation theory to naturally\nemerge from the Hilbert space representations in the Weyl quantization.",
"arxiv_id": "quant-ph/0011076",
"authors": [
"T. Hakioglu"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"hep-th",
"math-ph",
"math.MP",
"nlin.CD",
"nlin.SI",
"physics.optics"
],
"title": "Extended covariance under nonlinear canonical transformation in Weyl quantization",
"url": "https://arxiv.org/abs/quant-ph/0011076"
},
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