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New treatment of the noncommutative Dirac equation with a Coulomb potential

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Lamine Khodja, Slimane Zaim

Mathematical Physics · Submitted 16 Oct 2011

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

The authors' main claim In the nonrelativistic limit a general form of the hamiltonian of the hydrogen atom is obtained, and we show that the noncommmutativity plays the role of spin and magnetic field which gives the hyper fine structure.

how it is stated · asserted 1.00 read the record →

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arXiv ID1110.3532 (version 5)
Pith IDDP7IH7B6, Pith's permanent record of this paper and its review
CitationLamine Khodja, Slimane Zaim. "New treatment of the noncommutative Dirac equation with a Coulomb potential." arXiv:1110.3532 (2011). https://pith.science/paper/DP7IH7B6
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The compiled record

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,989 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v5. Results and the main claim are underlined; .

Using the approach the modified Euler-Lagrange field equation together with the corresponding Seiberg-Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative modification the energy levels and the possible new transitions. In the nonrelativistic limit a general form of the hamiltonian of the hydrogen atom is obtained, and we show that the noncommmutativity plays the role of spin and magnetic field which gives the hyper fine structure.

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 Using the approach the modified Euler-Lagrange field equation together with the corresponding Seiberg-Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. method 0.71 0.94 0.12 asserted 1.00
s1 We then find the noncommutative modification the energy levels and the possible new transitions. result 0.67 0.95 0.20 asserted 0.94
s2 In the nonrelativistic limit a general form of the hamiltonian of the hydrogen atom is obtained, and we show that the noncommmutativity plays the role of spin and magnetic field which gives the hyper fine structure. result 0.73 0.94 0.60 asserted 1.00

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

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  • arXiv listing abstract v5
not examined
  • full text
  • figures and tables
  • references and citing sentences
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  • T body sentences
  • C citations
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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

Using the approach the modified Euler-Lagrange field equation together with the corresponding Seiberg-Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative modification the energy levels and the possible new transitions. In the nonrelativistic limit a general form of the hamiltonian of the hydrogen atom is obtained, and we show that the noncommmutativity plays the role of spin and magnetic field which gives the hyper fine structure.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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