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

We present an analytical study of a fermion-antifermion ( ff̄ f f ¯ ) system governed by a two-body Dirac equation (TBDE) in $$(2+1)$$ ( 2 + 1 ) -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.