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

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M. Asorey, P. Facchi, V.I. Man'ko, G. Marmo, S. Pascazio, E.G.C. Sudarshan

Mathematical Physics · Submitted 28 Mar 2007

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv IDmath-ph/0703081 (version 1)
Pith IDJJZPGUPH, Pith's permanent record of this paper and its review
CitationE.G.C. Sudarshan, G. Marmo, M. Asorey, P. Facchi, S. Pascazio, V.I. Man'ko. "Radon transform on the cylinder and tomography of a particle on the circle." arXiv:math-ph/0703081 (2007). https://pith.science/paper/JJZPGUPH
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,014 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.05 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.32 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The tomographic probability distribution on the phase space (cylinder) related to a circle or an interval is introduced. contribution 0.99 0.81 0.19 asserted 0.99
s1 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. result 0.77 0.90 0.36 asserted 1.00
s2 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. contribution 0.88 0.86 0.21 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.72 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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.

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