Related papers: Dirac oscillator with nonzero minimal uncertainty …
Basically (2 + 1) dimensional Dirac equation with real deformed Lorentz scalar potential is investi gated in this study. The position dependent Fermi velocity function transforms Dirac Hamiltonian into a Klein-Gordon-like effective…
We consider the consistent deformation of the relativistic quantum mechanics introducing the noncommutativity of the space-time and preserving the Lorentz symmetry. The relativistic wave equation describing the spinning particle on…
A 3-dimensional non-commutative oscillator with no mass term but with a certain momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The latter corresponds to a Dirac…
In this paper, we determine the relativistic bound-state solutions for the charged (DO) Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime in $(2+1)$-dimensions, where such solutions are given by the two-component…
The traditional approach to accelerator optics, based mainly on classical mechanics, is working excellently from the practical point of view. However, from the point of view of curiosity, as well as with a view to explore quantitatively the…
The main goal of this work is to study the Dirac oscillator as a quantum field using the canonical formalism of quantum field theory and to develop the canonical quantization procedure for this system in $(1+1)$ and $(3+1)$ dimensions. This…
In the light of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation in two dimensions is established as a relation between the total number $n_{j}$ of the bound states and the sum of the phase shifts…
Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are…
We study the behavior of perturbations of small nonlinear Dirac standing waves. We assume that the linear Dirac operator of reference $H=D_m+V$ has only two double eigenvalues and that degeneracies are due to a symmetry of $H$ (theorem of…
In this paper, we examine the electron interaction within tilted anisotropic Dirac materials when subjected to external electric and magnetic fields possessing translational symmetry. Specifically, we focus on a distinct non-zero electric…
We demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasi-exactly solvable systems. Electric field configurations permitting quasi-exact…
The behavior of spin-1/2 particle in a weak static gravitational field is considered. The Dirac Hamiltonian is diagonalized by the Foldy-Wouthuysen transformation providing also the simple form for the momentum and spin polarization…
In the present article we show that the energy spectrum of the one-dimensional Dirac equation, in the presence of an attractive vectorial delta potential, exhibits a resonant behavior when one includes an asymptotically spatially vanishing…
Starting with a new theory of symmetries generated by isometries in field theories with spin, one finds the generators of the spinor representation in backgrounds with a given symmetry. In this manner one obtains a collection of conserved…
It is shown that in the case of the spherically symmetric static backgrounds there is a gauge in which the Dirac equation is manifestly covariant under rotations. This allows us to separate the spherical variables like in the flat…
We introduce the new, exactly solvable model of the two-dimensional Dirac fermion in presence of an asymmetric, P\"oschl-Teller-like vector potential. Utilizing the translation invariance of the system, the effective one-dimensional…
In the present work we obtain a new representation for the Dirac oscillator based on the Clifford algebra $C\ell_7.$ The symmetry breaking and the energy eigenvalues for our model of the Dirac oscillator are studied in the non-relativistic…
We investigate the semiclassical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the $\alpha$ matrices to the spin-$S$ matrices and doing a certain scaling, we…
In terms of the relational approach to space-time geometry and physical interactions, we show that the Dirac equation for a free fermion in the momentum representation can be obtained starting from a binary system of complex relations…
We consider the one-dimensional Dirac equation for the harmonic oscillator and the associated second order separated operators giving the resonances of the problem by complex dilation. The same operators have unique extensions as closed…