Amelino-Camelia Dsr Effects on Landau Levels of Dirac Pairs with Non-Minimal Coupling

Abstract

We present an analytical study of a fermion-antifermion (ff\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\overline{f}$$\end{document}) system governed by a two-body Dirac equation (TBDE) in (2+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(2+1)$$\end{document}-dimensional Minkowski spacetime, incorporating Dirac oscillator (DO) interactions and a uniform magnetic field. We work within Amelino-Camelia's framework, capturing leading-order Planck-scale effects while preserving the TBDE's first-order structure. Separation of center-of-mass and relative coordinates reduces the problem to a Whittaker-type radial equation, yielding a closed-form energy spectrum. DSR induces uniform energy shifts that grow with radial excitation but preserve mass symmetry between particle and antiparticle. A critical magnetic field is identified, at which Planck-scale effects vanish and the spectrum collapses to the rest mass threshold, indicating suppressed spatial resolution. These findings provide a consistent platform for probing Planckian signatures in relativistic bound states and affirm the robustness of spectral symmetries under DSR.