Amelino-camelia DSR effects on Landau levels of Dirac pairs with non-minimal coupling

Abstract We present an analytical study of a fermion-antifermion ( $$f\overline{f}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mover> <mml:mi>f</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> ) system governed by a two-body Dirac equation (TBDE) in $$(2+1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -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.