2026/02/25 by Abdelmalek Boumali, Nosratollah Jafari · 1 voice
Physics and Astronomy · #hep-th #physics.gen-ph
paper · pdf · doi:10.1140/epjc/s10052-026-15796-9
% Doubly Special Relativity (DSR) introduces, besides the invariant speed of light c, an observer-independent high-energy % scale that deforms relativistic kinematics and can be implemented through modified dispersion relations or effective % wave equations with energy-dependent spatial operators. In this work we develop a three-dimensional, exactly solvable % benchmark for such deformations in the spin-\tfrac12 sector: the Dirac oscillator. Following the original % construction of Moshinsky and Szczepaniak, the oscillator is introduced through a linear non-minimal momentum coupling, % which preserves Hermiticity and yields, after decoupling the Dirac equation into large and small components, a % three-dimensional isotropic harmonic-oscillator operator supplemented by a strong spin--orbit term. % We then incorporate Planck-scale deformations in two standard DSR realizations (Amelino--Camelia and % Magueijo--Smolin, characterized by an invariant energy scale k) and in a generalized DSR framework based on a % first-order expansion in the Planck length lp. In all cases the bound-state eigenfunctions retain the % oscillator-spinor structure dictated by spherical symmetry, while DSR deforms the algebraic relation between quantum % numbers (N,j,ℓ) and the relativistic energy, producing branch-dependent shifts for both particle and antiparticle % solutions. The undeformed limit (k→∞ or lp→0) is recovered smoothly and the deformation signal increases % with excitation through the oscillator scale and spin--orbit splitting.