Nonlocal Generalized Dirac Oscillators in (1 + 1) Dimensions
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Quantum Physics arXiv:2603.06717 (quant-ph) [Submitted on 5 Mar 2026] Title:Nonlocal Generalized Dirac Oscillators in (1 + 1) Dimensions Authors:Abdelmalek Boumali View a PDF of the paper titled Nonlocal Generalized Dirac Oscillators in (1 + 1) Dimensions, by Abdelmalek Boumali View PDF HTML (experimental) Abstract:We propose a nonlocal extension of the generalized Dirac oscillator (GDO) in $(1+1)$ dimensions by replacing the multiplicative interaction $f(x)$ with an integral operator $\hat F$ with kernel $f(x,x')$. The resulting Dirac equation preserves an operator factorization and decouples into two nonlocal Schrödinger-type (Sturm--Liouville) equations for the spinor components. We derive explicit expressions for the associated supersymmetric partner kernels in terms of $f$ and its derivatives, and we show that a complex-translation metric $\eta=e^{-\theta p_x}$ leads to a simple sufficient \emph{kernel-level} pseudo-Hermiticity constraint, $f(x+\ii\hbar\theta,x'+\ii\hbar\theta)=f^*(x',x)$, extending the familiar local complex-shift criteria. To provide a transparent \emph{nonlocal-to-local} interpretation, we adapt the Coz--Arnold--MacKellar current-based localization to each component equation, obtaining energy-dependent equivalent local potentials and multiplicative Perey (damping) factors. The mapping breaks down precisely at current zeros, thereby diagnosing the spurious solutions of the corresponding nonlocal Schrödinger problem. Finally, we illustrate the formalism with analytically tractable benchmarks (the local Dirac oscillator and a translation-invariant kernel) and with a finite-rank separable model (Gaussian form factor) that reduces the integro-differential problem to a small set of coupled ordinary differential equations and algebraic constraints. Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2603.06717 [quant-ph] (or arXiv:2603.06717v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.06717 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Abdelmalek Boumali [view email] [v1] Thu, 5 Mar 2026 22:20:05 UTC (15 KB) Full-text links: Access Paper: View a PDF of the paper titled Nonlocal Generalized Dirac Oscillators in (1 + 1) Dimensions, by Abdelmalek BoumaliView 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?)