Related papers: Gauge-invariant cutoff for Dirac electron systems …
In this paper we will attempt to show that the Dirac theory lends itself to an interpretation in terms of a unified sub-quantum mechanical field theory where, the fundamental force fields are weak electric and weak magnetic fields. We…
Searching for new states of matter and unusual quasiparticles in emerging materials and especially low-dimensional systems is one of the major trends in contemporary condensed matter physics. Dirac materials, which host quasiparticles which…
We analyze mass renormalization in massive Dirac-like systems in (2+1) dimensions arising from electron-phonon interactions at finite temperatures, employing the large-$N$ expansion. Our model combines the low-energy description of charge…
We consider the Lee-Wick (LW) finite electrodynamics, i.e., the U(1) gauge theory where a (gauge-invariant) dimension-6 operator containing higher-derivatives is added to the free Lagrangian of the U(1) sector. Three bounds on the LW heavy…
A study of fundamental geometrical interactions shows that the Dirac electron can be represented as a conformal wave. A Riemannian space is used, having coordinates that transform locally as spinors. The wave function becomes a gradient.…
A wide range of materials like graphene, topological insulators and transition metal dichalcogenides (TMDs) share an interesting property: the low energy excitations behave as Dirac particles. This emergent behavior of Dirac quasiparticles…
It is argued that in Weyl electrovacuum solutions the linear term in the metric cannot be eliminated just on grounds of gauge invariance. Its importance is stressed.
For computing thermodynamics of the electroweak phase transition, we discuss a minimal approach that reconciles both gauge invariance and thermal resummation. Such a minimal setup consists of a two-loop dimensional reduction to…
A gauge transformation in quantum electrodynamics involves the product of field operators at the same space-time point and hence does not have a well-defined meaning. One way to avoid this difficulty is to generalize the gauge…
In the variational framework, we study the electronic energy spectrum of massless Dirac fermions of graphene subjected to one-dimensional oscillating magnetic and electrostatic fields centered around a constant uniform static magnetic…
The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…
The time-dependent, geometric method for high-energy limits and inverse scattering is applied to nonrelativistic quantum particles in external electromagnetic fields. Both the Schr"odinger- and the Pauli equations in R^2 and R^3 are…
Gauge-invariance is a mathematical concept that has profound implications in Physics---as it provides the justification of the fundamental interactions. It was recently adapted to the Cellular Automaton (CA) framework, in a restricted case.…
The superconducting proximity effect on two-dimensional massless Dirac electrons is usually analyzed using a simple model consisting of the Dirac Hamiltonian and an energy-independent pair potential. Although this conventional model is…
Dirac semimetal is a class of semi-metallic phase protected by certain types of crystalline symmetries, and its low-energy effective Hamiltonian is described by Dirac equations in three dimensions (3D). Despite of various theoretical…
We have investigated the fractional quantum Hall states for the Dirac electrons in a graphene layer in different Landau levels. The relativistic nature of the energy dispersion relation of the electrons in the graphene significantly…
The problem of constructing gauge invariant currents in terms of light-cone bound-state wave functions is solved by utilising the gauging of equations method. In particular, it is shown how to construct perturbative expansions of the…
Fractional Dirac materials (FDMs) feature a fractional energy-momentum relation $E(\vec{k}) \sim |\vec{k}|^{\alpha}$, where $\alpha \; (<1)$ is a real noninteger number, in contrast to that in conventional Dirac materials with $\alpha=1$.…
One propose a relativistic version of the transfer matrix method for an electron moving through a given number of rectangular barriers of arbitrary shape. It is shown that starting with the Dirac equation depending on the effective mass and…
A study of the formation of excitons as a problem of two Dirac particles in a gapped graphene layer and in two gapped graphene layers separated by a dielectric is presented. In the low energy limit the separation of the center-of-mass and…