On the $\kappa$-Dirac Oscillator revisited

Abstract

This Letter is based on the $\kappa$-Dirac equation, derived from the $\kappa$-Poincaré-Hopf algebra. It is shown that the $\kappa$-Dirac equation preserves parity while breaks charge conjugation and time reversal symmetries. Introducing the Dirac oscillator prescription, $\mathbf{p}\to \mathbf{p}-im\omega \beta \mathbf{r}$, in the $\kappa$-Dirac equation, one obtains the $\kappa$-Dirac oscillator. Using a decomposition in terms of spin angular functions, one achieves the deformed radial equations, with the associated deformed energy eigenvalues and eigenfunctions. The deformation parameter breaks the infinite degeneracy of the Dirac oscillator. In the case where $\epsilon =0$, one recovers the energy eigenvalues and eigenfunctions of the Dirac oscillator.

5 pages, no figures, accepted for publication in Physics Letters B

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• Noninertial effects on the quantum dynamics of scalar bosons
• Effects of spin on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background
• Quantum dynamics of scalar bosons in a cosmic string background
• Three-dimensional Dirac oscillator in a thermal bath
• On the 2D Dirac oscillator in the presence of vector and scalar potentials in the cosmic string spacetime in the context of spin and pseudospin symmetries
• Bound state solutions of the Dirac oscillator in an Aharonov-Bohm-Coulomb system
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• The 2D $\kappa$-Dirac oscillator
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Generalized Dirac Oscillators with position-dependent mass
• The influence of Aharonov-Casher effect on the generalized Dirac oscillator in the cosmic string space-time
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Two-dimensional pauli equation in noncommutative phase-space
• Effects of quantum deformation on the integer quantum Hall effect
• Amelino-Camelia DSR effects on charged Dirac oscillators: Modulated spinning magnetic vortices
• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
• Kappa-deformed Dirac oscillator in an external magnetic field
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Reproducing the effects of quantum deformation in the undeformed Jaynes-Cummings model