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arXiv:math-ph/0703081 · Physical Review A

Radon transform on the cylinder and tomography of a particle on the circle

M. Asorey, Paolo Facchi A, Vladimir I. Man’ko, Giuseppe Marmo, Saverio Pascazio, E. C. G. Sudarshan

Published Jul 24, 2007• 24 citations
arXivHTMLPDF

Abstract

The tomographic probability distribution on the phase space (cylinder) related to a circle or an interval is introduced. The explicit relations of the tomographic probability densities and the probability densities on the phase space for the particle motion on a torus are obtained, and the relation of the suggested map to the Radon transform on the plane is elucidated. The generalization to the case of a multidimensional torus is elaborated, and the geometrical meaning of the tomographic probability densities as marginal distributions on the helix discussed.

DOI
10.1103/physreva.76.012117

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The tomographic probability distribution on the phase space (cylinder) related to a circle or an interval is introduced. The explicit relations of the tomographic probability densities and the probability densities on the phase space for the particle motion on a torus are obtained, and the relation of the suggested map to the Radon transform on the plane is elucidated. The generalization to the case of a multidimensional torus is elaborated, and the geometrical meaning of the tomographic probability densities as marginal distributions on the helix discussed.
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