Related papers: Energy quantization at the "three-quarter Dirac po…
We compute the energy spectrum of the ground state of a 2D Dirac electron in the presence of a Coulomb potential and a constant magnetic field perpendicular to the plane where the the electron is confined. With the help of a mixed-basis…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
The exact solution of the Dirac equation and the spectrum of electron quasi-energies in a superposition of the field of a circularly polarized electromagnetic wave and a homogeneous magnetic field parallel to the direction of wave…
This work aims to shed some light on the meaning of the positive energy assumption in relativistic quantum theory and its relation to questions of localization of quantum systems. It is shown that the positive energy property of solutions…
Delocalization problem for a two-dimensional non-interacting electron system is studied under a random magnetic field. With the presence of a random magnetic field, the Hall conductance carried by each eigenstate can become nonzero and…
We derive a general expression for the fermion self-energy in a hot magnetized plasma by using the Landau-level representation. In the one-loop approximation, the Dirac structure of the self-energy is characterized by five different…
We consider a relativistic hydrogenic atom in a strong magnetic field. The ground state level depends on the strength of the magnetic field and reaches the lower end of the spectral gap of the Dirac-Coulomb operator for a certain critical…
Levinson's theorem for the Dirac equation is known in the form of a sum of positive and negative energy phase shifts at zero momentum related to the total number of bound states. In this letter we prove a stronger version of Levinson's…
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…
Since the discovery of the Fractional Quantum Hall Effect in 1982 there has been considerable theoretical discussion on the possibility of fractional quantization of conductance in the absence of Landau levels formed by a quantizing…
A Friedmann--Robertson--Walker Universe is studied with a dark energy component represented by a quintessence field. The Lagrangian for this system, hereafter called the Friedmann--Robertson--Walker--quintessence (FRWq) system, is…
We study the quantum Hall effect of 2D electron gas in black phosphorus in the presence of perpendicular electric and magnetic fields. In the absence of a bias voltage, the external magnetic field leads to a quantization of the energy…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
We study the (2+1)-dimensional Dirac oscillator in the presence of an external uniform magnetic field ($B$). We show how the change of the strength of $B$ leads to the existence of a quantum phase transition in the chirality of the system.…
Systematic description of a spin one-half system endowed with magnetic moment or any other two-level system (qubit) interacting with the quantized electromagnetic field is developed. This description exploits a close analogy between a…
We study the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field in the non-commutative plane. It is shown that the effect of non-commutativity is twofold: $i$) momentum non commuting coordinates simply shift the critical…
We examine a covariant quantization of electromagnetic fields by using an operator derived from a constant scalar that can be called extended Lorentz gauge. The quantization can avoid an inconsistency between Lorentz gauge and a commutation…
It was long believed that there is a zero-point energy in the form of h\omega/2 for massive particles, which is obtained from Schr\"odinger equation for the harmonic oscillator model. In this paper, it is shown, by the Dirac oscillator,…
As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present…
Relativistic fermionic field theories constitute the fundamental description of all observable matter. The simplest of the models provide a useful, classically verifiable benchmark for noisy intermediate scale quantum computers. We…