The κ-deformation of the generalized DKP oscillator

Abstract

We consider the Duffin–Kemmer–Petiau (DKP) oscillator for spin-zero bosons, coupled to a pseudoscalar Coulomb potential, in a (3+1)-dimensional noncommutative space–time characterized by κ-deformation. We use the method of Dirac derivatives to build the κ-deformed DKP equation. We work out the solutions of the generalized oscillator so obtained using a perturbation method: This allowed to examine first-order effects of the non-commutativity on its eigenenergies and eigenfunctions. Notably, we find that, due to the deformation, the energy levels of s-states become discontinuous at a certain critical value of the coupling constant of the Coulomb term. We also note an asymmetry between particle and antiparticle energies revealing the breaking of the charge-conjugation symmetry for deformed DKP equation. In addition, we discuss the κ-deformed DKP oscillator as a particular case of the considered model.

Keywords

• Generalized DKP oscillator
• Non-commutativity
• Theoretical study