Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction

We introduce a unique model for a fermion antifermion pair interacting through Dirac oscillator interaction in the presence of external uniform magnetic field. In order to acquire a non perturbative energy spectrum for such a system we solve the corresponding form of a fully covariant two body Dirac equation. The dynamic symmetry of the system allows to study in three dimensions and the corresponding equation leads a $4\times4$ dimensional matrix equation for such a static and spinless composite system. We can obtain an exact solution of the matrix equation and arrive at a spectrum (in closed form) in energy domain. The obtained energy spectrum shows that the composite system that under scrutiny behaves like a single relativistic quantum oscillator. As a result, we obtain relativistic Landau levels of a fermion antifermion pair interacting through Dirac oscillator interaction and determine the components of the corresponding bi-spinor. We think that our results can provide enlightening informations about the quark antiquark systems and thus mass formula for mesons.Comment: 1 figur

The relativistic dynamics of oppositely charged two fermions interacting with external uniform magnetic field

We investigated the relativistic dynamics of oppositely charged two fermions interacting with an external uniform magnetic field. We chose the interaction of each fermion with the external magnetic field in the symmetric gauge, and obtained a precise solution of the corresponding fully-covariant two-body Dirac equation that derived from Quantum Electrodynamics via Action principle. The dynamic symmetry of the system we deal with allowed us to determine the relativistic Landau levels of such a spinless composite system, without using any group theoretical method. As a result, we determined the eigenfunctions and eigenvalues of the corresponding two-body Dirac HamiltonianComment: 1 figur

Exact solution of an exciton energy for a monolayer medium

We present exact solutions of an energy spectrum of 2-interacting particles in which they seem to be relativistic fermions in 2+1 space-time dimensions. The 2x2 spinor equations of 2-interacting fermions through general central potential were separated covariantly into the relative and center of mass coordinates. First of all, the coupled first order differential equations depending on radial coordinate were derived from 2x2 spinor equations. Then, a second order radial differential equation was obtained and solved for Coulomb interaction potential. We apply our solutions to exciton phenomena for a free-standing monolayer medium. Since we regard exciton as isolated 2-interacting fermions in our model, any other external effect such as substrate was eliminated. Our results show that the obtained binding energies in our model are in agreement with the literature. Moreover, the decay time of an exciton was found out spontaneously in our calculations.Comment: 5 page

Quasibound states for scalar field under the influence of an external magnetic field in the near-horizon geometry of the BTZ black hole with torsion

We consider a scalar field under the effect of external magnetic field in thenear-horizon geometry of the Banados-Teitelboim-Zanelli black hole with torsionand obtain quasistationary states of the system under consideration by solvingthe corresponding Klein-Gordon equation. We obtain exact solution of theequation and accordingly we arrive at a complex spectra. We observe that thereal oscillation frequency of the modes and their decay time depend on thestrength of external magnetic field besides the parameters of geometricbackground. We see that amplitude of the real oscillation modes decreases anddecay time of the modes becomes longer as the strength of the external magneticfield increases. The results indicate that the geometric background is stableunder such a perturbation field

Quasibound states for a scalar field under the influence of an external magnetic field in the near-horizon geometry of the BTZ black hole with torsion

We consider a charged scalar field under the effect of an external uniform magnetic field in the near-horizon geometry of the Banados-Teitelboim-Zanelli black hole with torsion and obtain quasi-stationary states of the system under consideration through obtaining analytical solution of the corresponding Klein-Gordon equation. We obtain the solution function of the equation and accordingly we arrive at complex spectra. We observe that the real oscillation frequency of the modes and their decay time depend on the strength of the external magnetic field beside the parameters of geometric background. We see that the amplitude of the real oscillation modes decreases and the decay time of the modes becomes longer as the strength of the external magnetic field increases. The results indicate that the geometric background is stable under such a perturbation field