Related papers: The Dirac Vacuum in Discrete Spacetime
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 study quantum effects of recently discovered kink solitons which are constructed self-consistently by coupling to a single, excited fermion bound state. Our studies are based on the observation that in a semi-classical expansion the…
Neutral fermions of spin $\frac 12$ with magnetic moment can interact with electromagnetic fields through nonminimal coupling. The Dirac--Pauli equation for such a fermion coupled to a spherically symmetric or central electric field can be…
The effects of the Dirac sea of the nucleons are investigated within a covariant model of the hadronic interaction. We extend the usual Mean Field Approximation and present a procedure to deal with divergences which are proportional to…
It is shown that the Dirac theory implies complex space-time and complex space-time can lead to the Dirac equation. It is suggested that fermions are grouped into doublets, those doublets are then divided into color singlets (leptons) and…
We investigate some properties of a system of Dirac fermions in 2+1 dimensions, with a space dependent mass having domain wall like defects.These defects are defined by the loci of the points where the mass changes sign. In general, they…
The $\sigma$-$\omega$ model of nuclei is studied at leading order in the $1/N$ expansion thereby introducing the self consistent Hartree approximation, the Dirac sea corrections and the one fermion loop meson self energies in a unified way.…
We consider Dirac equation in $(2+1)$ dimensional curved spacetime in the presence of a scalar potential. It is then shown that the zero energy states are degenerate and they can be obtained when the momentum $k_y$ in the $y$ direction…
Negative energy densities in the Dirac field produced by state vectors that are the superposition of two single particle electron states are examined. I show that for such states the energy density of the field is not bounded from below and…
It was shown in work \cite{vergeles2021note} that in the theory of gravity coupled with the Dirac field, each state $|\lambda\rangle$ has its own twin $|\lambda;PT\rangle$, which is obtained by a discrete PT transformation. If in the state…
A simple and reliable finite difference approach is presented for solution of the Dirac equation eigenproblem for states confined in rotationally symmetric systems. The method sets the boundary condition for the spinor wave function…
In Dirac's hole theory the vacuum state is assumed to be the state where all negative energy states are occupied and all positive energy states are unoccupied. This is often referred to as the Dirac sea. It is generally assumed that the…
We present a pilot-wave model for quantum field theory in which the Dirac sea is taken seriously. The model ascribes particle trajectories to all the fermions, including the fermions filling the Dirac sea. The model is deterministic and…
This work is motivated by the long-standing question about the internal stability of the electron. While one cannot investigate internal properties of a point-like particle, it is fair to analyze the response of the Dirac sea to an…
We examine the one dimensional Dirac equation with modulated or position dependent velocity. In particular, it is shown that using suitable velocity profiles it is possible to create bound state in continuum (BIC) like, as well as, discrete…
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…
Random Dirac fermions in a two-dimensional space are studied numerically. We realize them on a square lattice using the $\pi$-flux model with random hopping. The system preserves two symmetries, the time-reversal symmetry and the symmetry…
We consider the long standing problem in field theories of bosons that the boson vacuum does not consist of a `sea', unlike the fermion vacuum. We show with the help of supersymmetry considerations that the boson vacuum indeed does also…
We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime…
A non-relativistic system such as an ultracold trapped ion may perform a quantum simulation of a Dirac equation dynamics under specific conditions. The resulting Hamiltonian and dynamics are highly controllable, but the coupling between…