Two-body Dirac equation in DSR: Results for fermion-antifermion pairs
Jafari N. Guvendi A.
July 2025Elsevier B.V.
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
2025#866
This study investigates a modified two-body Dirac equation in 2+1-dimensional spacetime, inspired by Amelino-Camelias 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 α behaves as an energy-dependent running parameter, given by [Formula presented], 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.
Binding energy , Doubly special relativity , Fermion-antifermion pair , Two-body problem
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Fesenkov Astrophysical Institute, Almaty, 050020, Kazakhstan
Al-Farabi Kazakh National University, Al-Farabi av. 71, Almaty, 050040, Kazakhstan
Center for Theoretical Physics, Khazar University, 41 Mehseti Street, Baku, AZ1096, Azerbaijan
Department of Basic Sciences, Erzurum Technical University, Erzurum, 25050, Turkey
Fesenkov Astrophysical Institute
Al-Farabi Kazakh National University
Center for Theoretical Physics
Department of Basic Sciences
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026