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arXiv:quant-ph/0604148 · Reports on Mathematical Physics

A tomographic setting for quasi-distribution functions

Vladimir I. Man’ko, Giuseppe Marmo, Alberto Simoni, E. C. G. Sudarshan, F. Ventriglia

Published Jun 1, 2008• 27 citations
arXivHTMLPDF
DOI
10.1016/s0034-4877(08)00016-5

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The gauge invariance of the evolution equations of tomographic probability distribution functions of quantum particles in an electromagnetic field is illustrated. Explicit expressions for the transformations of ordinary tomograms of states under a gauge transformation of electromagnetic field potentials are obtained. Gauge-independent optical and symplectic tomographic quasi-distributions and tomographic probability distributions of states of quantum system are introduced, and their evolution equations having the Liouville equation in corresponding representations as the classical limit are found.
Abstract The gauge invariance of the evolution equations of tomographic probability distribution functions of quantum particles in an electromagnetic field is illustrated. Explicit expressions for the transformations of ordinary tomograms of states under a gauge transformation of electromagnetic field potentials are obtained. Gauge-independent optical and symplectic tomographic quasi-distributions and tomographic probability distributions of states of quantum system are introduced, and their evolution equations have the Liouville equation in corresponding representations as the classical limits are found.
We present a method of constructing the tomographic probability distributions describing quantum states in parallel with density operators in abstract Hilbert spaces. After the study of an infinite dimensional example, the well known Husimi-Kano quasi-distribution is reconsidered in the new setting and a new tomographic scheme based on coherent states is suggested. Starting from the Sudarshan's diagonal coherent state representation, the associated identity decomposition providing Gram-Schmidt operators is explicitly given.