Radon transform on the cylinder and tomography of a particle on the circle
arXiv:math-ph/0703081 · doi:10.1103/PhysRevA.76.012117
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.
9 pages, 3 figures
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