Related papers: Random Dirac Fermions and Non-Hermitian Quantum Me…
We obtain an exact solution of the Dirac equation in (2+1)-dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. The solution space consists of a…
The Dirac theory implies the existence of an internal vector space, in addition to spin space. Using Dirac's coupling of variables in internal space to those in physical space, we construct a new configuration structure for particles in the…
We present a new approach to study a class of non-Hermitian (1+1)-dimensional Dirac Hamiltonian in the presence of local Fermi velocity. We apply the well known Nikiforov-Uvarov method to solve such a system. We discuss applications and…
In this manuscript, we study the relativistic quantum mechanics of an electron in external fields in the spinning cosmic string spacetime. We obtain the Dirac equation, write the first and second-order equations from it, and then we solve…
The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic…
The generalized Dirac equation of the second order, describing particles with spin 1/2 and two mass states, is analyzed. The projection operators extracting states with definite energy and spin projections are obtained. The first order…
The Dirac equation requires a treatment of the step potential that differs fundamentally from the traditional treatment, because the Dirac plane waves, besides momentum and spin, are characterized by a quantum number with the physical…
We focus on the confinement of two-dimensional Dirac fermions within the waveguides created by realistic magnetic fields. Understanding of their band structure is of our main concern. We provide easily applicable criteria, mostly depending…
In this paper we construct a non-commutative geometry over a configuration space of gauge connections and show that it gives rise to a candidate for an interacting, non-perturbative quantum gauge theory coupled to a fermionic field on a…
I investigate three dimensional abelian and non-abelian gauge theories interacting with Dirac fermions. Using a variational method I evaluate the vacuum energy density in the one-loop approximation. It turns out that the states with a…
We apply the Dirac factorization method to the nonrelativistic harmonic oscillator and, more in general, to Hamiltonians with a generic potential. It is shown that this procedure naturally leads to a supersymmetric formulation of the…
The modified Dirac-Pauli equations, which are introduced by means of ${\gamma_5}$-mass factorization of the ordinary Klein-Gordon operator, are considered. We also take into account the interaction of fermions with the intensive homogenous…
A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of…
In recent years, an extensive survey on various wave equations of relativistic quantum mechanics with different types of potential interactions has been a line of great interest. In this regime, special attention has been given to the Dirac…
The damping rate of two-dimensional massless Dirac fermions exhibit non-Fermi liquid behavior, $\propto \epsilon^{1/2}$, due to gauge field at zero temperature and zero chemical potential. We study the fate of this behavior at finite…
In this work, a spin $\frac 12$ relativistic particle described by a generalized potential containing both the Coulomb potential and a Lorentz scalar potential in Dirac equation is investigated in terms of the generalized ladder operators…
Proofs of two statements are provided in this paper. First, the authors prove that the formalism of the pseudo-Hermitian quantum mechanics allows describing the Dirac particles motion in arbitrary stationary gravitational fields. Second, it…
The mechanism of delocalization of two-dimensional Dirac fermions with random mass is investigated, using a superfield representation. Although localization effects are very strong, one fermion component can delocalize due to the…
We study the confinement of charged Dirac particles in 3+1 space-time due to the presence of a constant and tilted magnetic field. We focus on the nature of the solutions of the Dirac equation and on how they depend on the choice of vector…
The axially symmetric $U(1)$ gauged self-interacting Q-balls are shown to support normalizable fermionic bound state, minimally coupled to the electromagnetic field of the Q-ball. It is shown that the effects of the backreaction of the…