Jafari, NosratollahGuvendi, Abdullah2026-03-262026-03-2620250370-26931873-244510.1016/j.physletb.2025.1395152-s2.0-105004054600https://doi.org/10.1016/j.physletb.2025.139515https://hdl.handle.net/20.500.14901/2390Güvendi, Abdullah/0000-0003-0564-9899This study investigates a modified two-body Dirac equation in 2+1-dimensional spacetime, inspired by AmelinoCamelia's doubly special relativity (DSR). We begin by deriving a covariant two-body Dirac equation that, in the absence of DSR modifications, reduces to a Bessel-type wave equation. Incorporating corrections from the chosen DSR model modifies this wave equation, yielding solutions consistent with established results in the low-energy regime. We demonstrate that the effects of DSR modifications become particularly pronounced at large relative distances. For a coupled fermion-antifermion pair, we derive the modified binding energy solutions. By accounting for first-order Planck-scale corrections, we show that the fine-structure constant a behaves as an energy-dependent running parameter, given by aeff(E)/a 1 - E 4EP, where EP is the Planck energy. Binding energy levels are computed using a first-order approximation of the DSR modifications, and the results are applied to positronium-like systems. Our model reveals that DSR modifications induce shifts in the binding energy levels. To the best of our knowledge, DSR-modified two-body equations have not been previously studied. This model is the first of its kind, opening new avenues for further research in this area.eninfo:eu-repo/semantics/openAccessDoubly Special RelativityFermion-Antifermion PairTwo-Body ProblemBinding EnergyArticle