Feshbach-Villars Hamiltonian Approach to the Klein-Gordon Oscillator and Supercritical Step Scattering in Standard and Generalized Doubly Special Relativity
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Quantum Physics arXiv:2601.18836 (quant-ph) [Submitted on 25 Jan 2026] Title:Feshbach-Villars Hamiltonian Approach to the Klein-Gordon Oscillator and Supercritical Step Scattering in Standard and Generalized Doubly Special Relativity Authors:A. Boumali, N. Jafari, Y. Chargui View a PDF of the paper titled Feshbach-Villars Hamiltonian Approach to the Klein-Gordon Oscillator and Supercritical Step Scattering in Standard and Generalized Doubly Special Relativity, by A. Boumali and 2 other authors View PDF HTML (experimental) Abstract:We develop a first-order Feshbach-Villars (FV) Hamiltonian framework for spin-0 relativistic quantum dynamics in the presence of Planck-scale kinematic deformations described within generalized doubly special relativity (G-DSR). Starting from a generic nonlinear momentum-space map, we derive the corresponding modified dispersion relation (MDR) at leading order in the Planck length \(l_p\) and construct a consistent FV linearization of the deformed Klein-Gordon operator. The resulting two-component Hamiltonian remains \(\sigma_3\)-pseudo-Hermitian at \(\mathcal{O}(l_p)\), which guarantees conservation of the FV charge and current and provides a current-based definition of reflection and transmission in stationary scattering. As applications, we study two benchmark settings in which the FV metric structure is essential: (i) the one-dimensional Klein-Gordon oscillator and (ii) scattering from electrostatic step and barrier potentials. For the oscillator, we obtain controlled \(\mathcal{O}(l_p)\) branch-resolved spectral shifts and show how kinetic versus mass-shell deformations reshape the level spacing and the high-energy spectral compression. For step and barrier scattering, we compute reflection and transmission coefficients directly from the pseudo-Hermitian FV current and quantify the deformation-induced shift of the supercritical (pair-production) threshold. A comparative analysis of the Amelino-Camelia and Magueijo-Smolin realizations indicates that MS-type deformations generally delay the onset of the supercritical regime and reduce the magnitude of the negative transmitted flux within the validity domain \(l_p E \ll 1\). Subjects: Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th) Cite as: arXiv:2601.18836 [quant-ph] (or arXiv:2601.18836v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.18836 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Abdelmalek Boumali [view email] [v1] Sun, 25 Jan 2026 20:57:45 UTC (1,021 KB) Full-text links: Access Paper: View a PDF of the paper titled Feshbach-Villars Hamiltonian Approach to the Klein-Gordon Oscillator and Supercritical Step Scattering in Standard and Generalized Doubly Special Relativity, by A. Boumali and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: gr-qc hep-th References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)