{"paper":{"title":"Testing $(q)$-Deformed Dunkl-Fokker-Planck Equation Algebra with Supersymmetry (SUSY) and Foldy-Wouthuysen (FW) Measurement","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"The (q)-deformed Dunkl-Fokker-Planck equation is extended to a relativistic supersymmetric framework in 1+1 dimensions using reflection symmetry and a generalized Foldy-Wouthuysen transformation.","cross_cats":[],"primary_cat":"hep-th","authors_text":"Abdelmalek Bouzenada","submitted_at":"2026-05-13T16:33:11Z","abstract_excerpt":"In this study, a relativistic formulation of the $(q)$-deformed Dunkl-Fokker-Planck equation in $(1+1)$-dimensions is constructed within the reflection-deformed quantum framework. In this case, the formalism includes $(q)$-deformed Dunkl operators and reflection symmetry to build a generalized dynamical structure for a relativistic quantum systems framework. Moreover, the corresponding $(q)$-Wigner-Dunkl supersymmetric configuration is established via the construction of deformed ladder operators and supersymmetric algebraic relations, yielding a consistent spectral representation of the model"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The analysis extends to the harmonic oscillator with centrifugal interaction, where exact algebraic solutions, similarity reduction techniques, and closed energy spectra are obtained analytically in detail.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the q-deformed Dunkl operators together with reflection symmetry can be consistently extended to a relativistic supersymmetric framework in 1+1 dimensions while preserving algebraic closure and yielding well-defined spectra without introducing inconsistencies.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A relativistic q-deformed Dunkl-Fokker-Planck equation is formulated with supersymmetry and reflection symmetry, yielding exact algebraic solutions for the harmonic oscillator and an effective Hamiltonian after Foldy-Wouthuysen reduction.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The (q)-deformed Dunkl-Fokker-Planck equation is extended to a relativistic supersymmetric framework in 1+1 dimensions using reflection symmetry and a generalized Foldy-Wouthuysen transformation.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9369a86e188f5604ecbcef620f0e1c3ad435e96055946a93038f4f464d86e00d"},"source":{"id":"2605.13938","kind":"arxiv","version":1},"verdict":{"id":"4d5fc9c4-e443-4bfa-85c9-a21a0a2a4399","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:50:34.355638Z","strongest_claim":"The analysis extends to the harmonic oscillator with centrifugal interaction, where exact algebraic solutions, similarity reduction techniques, and closed energy spectra are obtained analytically in detail.","one_line_summary":"A relativistic q-deformed Dunkl-Fokker-Planck equation is formulated with supersymmetry and reflection symmetry, yielding exact algebraic solutions for the harmonic oscillator and an effective Hamiltonian after Foldy-Wouthuysen reduction.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the q-deformed Dunkl operators together with reflection symmetry can be consistently extended to a relativistic supersymmetric framework in 1+1 dimensions while preserving algebraic closure and yielding well-defined spectra without introducing inconsistencies.","pith_extraction_headline":"The (q)-deformed Dunkl-Fokker-Planck equation is extended to a relativistic supersymmetric framework in 1+1 dimensions using reflection symmetry and a generalized Foldy-Wouthuysen transformation."},"references":{"count":136,"sample":[{"doi":"","year":2011,"title":"Greiner,Quantum mechanics: an introduction, Springer Science (2011)","work_id":"37cc6370-55d3-4c33-bfd0-e2ad4093c3aa","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1916,"title":"A. Einstein, Ann. Phys.,49(7), 769-822 (1916)","work_id":"757f96ce-10be-4a57-bf04-1fa0c8223fdb","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"C. Rovelli, Living. Rev. Relativ.,11, 1-69 (2008)","work_id":"c92a2957-9b83-4693-a91c-3e3956d590b3","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1926,"title":"O. Klein, Z. Physik37, 895-906 (1926)","work_id":"6729a329-1b41-4e2c-bab2-12b1ef5e3ea6","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1928,"title":"P. A. M. Dirac, Proc R Soc London, Ser A,117(778), 610-624 (1928)","work_id":"0df30897-3536-412f-a8f4-bf88b4ffab7c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":136,"snapshot_sha256":"c5572e35021dec647e48ffe1b86419dc816ba7a40b10f4dc306c88591080b42d","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"7cf2eb25ba4c64f182c5fef93fcf8bd08220b7aedf61d44871e1a203223254a8"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}