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We study $(2+1)$ dimensional Dirac equation with complex scalar and Lorentz scalar potentials. It is shown that the Dirac equation admits exact analytical solutions with real eigenvalues for certain complex potentials while for another…
Applications of the Dirac equation with an anomalous magnetic moment are considered for description of characteristics of electrons, muons and quarks. The Dirac equation with four-dimensional scalar and vector potentials is reduced to a…
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \mapsto \infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the…
The extended Cornell potential which the harmonic oscillator potential is included in the original Cornell potential. The Dirac equation is solved by reducing the Dirac equation to the form of Schrodinger equation. The Nikiforov-Uvarov…
In the present paper, we solve the Dirac equation in the 2+1 dimensional exponentially expanding magnetized by uniform magnetic field and non-magnetized universes, separately. Asymptotic behaviors of the solutions are determined. Using…
Starting with the Dirac equation for an electron in a constant electromagnetic background on a noncommutative (NC) plane, we obtain a gauge invariant description of the system. Surprisingly, the dynamics of the system is dictated by the…
We introduce a Dirac equation which reproduces the usual radial sextic oscillator potential in the non-relativistic limit. We determine its energy spectrum in the presence of the magnetic field. It is shown that the equation is solved in…
We discuss the generalization of the Dirac equations and spinors in momentum space to free unstable spin-$1/2$ fermions taking into account the fundamental requirement of Lorentz covariance. We derive the generalized adjoint Dirac equations…
The so-called Dirac oscillator was proposed as a modification of the free Dirac equation which reproduces many of the properties of the simple harmonic oscillator but accompanied by a strong spin-orbit coupling term. It has yet to be…
We introduce a new equation we dubbed the modular Dirac equation to see and reconstruct a spin 1/2 particle at the center of a nearly $AdS_2$ spacetime in the entanglement wedge reconstruction paradigm and we study hidden symmetries of this…
In this paper we have considered the dynamics of an anomalous ($g\neq 2$) charged relativistic spinning particle in the presence of an external electromagnetic field. The constraint analysis is done and the complete set of Dirac brackets…
We consider a classical Dirac field in flat Minkowski spacetime. We perform a Gordon decomposition of its canonical energy-momentum and spin currents, respectively. Thereby we find for each of these currents a convective and a polarization…
A modified system of equations of electrodynamics has been obtained. Beside the Lagrangian one an alternative gauge-like formalism has been developed to introduce the toroid moment contributions in the equations obtained. The two potential…
The Dirac equation is invariant under rotations with a constant frequency and invariable cylindrical radius. 3D transformation for rotating frames is found with help of this invariance. Exact localized solutions of the Dirac equation in the…
The gravitational couplings of intrinsic spin are briefly reviewed. A consequence of the Dirac equation in the exterior gravitational field of a rotating mass is considered in detail, namely, the difference in the energy of a spin-1/2…
The second-order modified Dirac equation leading to the modified dispersion relation due to the Lorentz invariance violation corrections is suggested. The equation is formulated in the 16-component first- order form. I have obtained the…
The Dirac approach to include magnetic charge in Maxwell's equations places the magnetic charge at the end of a string on which the the fields of the theory develop a singularity. In this paper an alternative formulation of classical…
By viewing the electron as a wavepacket in the positive energy spectrum of the Dirac equation, we are able to achieve a much clearer understanding of its behavior under weak electromagnetic fields. The intrinsic spin magnetic moment is…
We consider the presence of odd powers of the speed of light $c$ in the covariant nonrelativistic expansion of General Relativity (GR). The term of order $c$ in the relativistic metric is a vector potential that contributes at leading order…
The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metrics leads to new contributions to the in-band energy operator in…