Klein--Gordon oscillator with linear--fractional deformed Casimirs in doubly special relativity
Summarize this article with:
Quantum Physics arXiv:2603.06637 (quant-ph) [Submitted on 24 Feb 2026] Title:Klein--Gordon oscillator with linear--fractional deformed Casimirs in doubly special relativity Authors:Abdelmalek Boumali, Nosratollah Jafari View a PDF of the paper titled Klein--Gordon oscillator with linear--fractional deformed Casimirs in doubly special relativity, by Abdelmalek Boumali and Nosratollah Jafari View PDF HTML (experimental) Abstract:We study the Klein--Gordon (KG) oscillator in a doubly special relativity (DSR) framework, where the mass-shell condition is deformed through a linear--fractional (Möbius-type) modification of the Casimir invariant. This is induced by a nonlinear map from physical momenta $p^\mu$ to auxiliary Lorentz-covariant variables $\pi^\mu$. In $(1+1)$ dimensions, the deformation is controlled by a constant covector $a_\mu$, yielding inequivalent realizations depending on whether $a_\mu$ is timelike, spacelike, or lightlike. Implementing the KG oscillator via a reverted-product nonminimal coupling, we obtain exact closed-form spectra and explicit eigensolutions for both particle and antiparticle branches across all three geometries. Timelike and lightlike deformations produce identical spectra characterized by a Planck-suppressed additive displacement. This breaks the exact $E\leftrightarrow -E$ symmetry via a term linear in $E$, interpretable as a branch-independent reparametrization of the energy origin. Conversely, the spacelike deformation is strictly isospectral to the undeformed oscillator but generates complex-shifted wavefunctions and a non-Hermitian spatial operator. We provide a compact $\mathcal{PT}$-symmetric and pseudo-Hermitian formulation by constructing an explicit similarity map $\mathcal{S}$ to a Hermitian oscillator, deriving the metric operator $\eta=\mathcal{S}^\dagger \mathcal{S}$, and establishing biorthonormal relations. Finally, we compare quantitatively with the Magueijo--Smolin (DSR2) model: the squared-denominator invariant leads to a larger Planck-suppressed displacement at fixed $m/E_{Pl}$, highlighting the denominator power's role in controlling spectral shifts. Representative plots illustrate the dependence on deformation ratio, oscillator strength, and excitation level. Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2603.06637 [quant-ph] (or arXiv:2603.06637v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.06637 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Abdelmalek Boumali [view email] [v1] Tue, 24 Feb 2026 22:58:53 UTC (39 KB) Full-text links: Access Paper: View a PDF of the paper titled Klein--Gordon oscillator with linear--fractional deformed Casimirs in doubly special relativity, by Abdelmalek Boumali and Nosratollah JafariView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: 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?)