Related papers: The Dirac Vacuum in Discrete Spacetime
In has been recently shown [1] that in Dirac's hole theory the vacuum state is not the minimum energy state but that there exist quantum states with less energy than that of the vacuum state. In this paper we extend this discussion to…
Self-consistent Hamiltonian formulation of scalar theory on the null plane is constructed following Dirac method. The theory contains also {\it constraint equations}. They would give, if solved, to a nonlinear and nonlocal Hamiltonian. The…
In generic curved spacetimes, the unavailability of a natural choice of vacuum state introduces a serious ambiguity in the Fock quantization of fields. In this review, we study the case of fermions described by a Dirac field in several…
We attempt to shed light on the following question: What happens to the negative energy states when we take the non-relativistic limit of the Dirac equation? The Levy-Leblond equation is the non-relativistic limit of the Dirac equation and…
At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also…
We study massless Dirac fermions in the background of a specific planar topologically nontrivial configuration in the three-dimensional spacetime. The results show the presence of massive bound states, phase shifts and the consequent…
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…
The tetrad gauge invariant theory of the free Dirac field in two special moving charts of the de Sitter spacetime is investigated pointing out the operators that commute with the Dirac one. These are the generators of the symmetry…
The gravitational-radiation-induced inspiral of a binary system of compact objects is considered. A scheme is described to model the regime in which the gravitational interaction is too strong to use weak-field approximation methods, but…
The stability of cosmological solutions in the recently suggested specific mechanism of dynamical compensation of vacuum energy is studied. It is found that the solutions in the original version lead to cosmological singularity which could…
We investigate a 6d Dirac fermion on a rectangle. It is found that the 4d spectrum is governed by $N=2$ supersymmetric quantum mechanics. Then we demonstrate that the supersymmetry is very useful for classifying all the allowed boundary…
We investigate nonlinear Dirac equations on a periodic quantum graph $G$ and develop a variational approach to the existence and multiplicity of bound states. After introducing the Dirac operator on $G$ with a $\mathbb Z^{d}$-periodic…
We consider a model of a quantized fermion field that is based on the Dirac equation in one dimensional space and re-examine how the fermion number of the vacuum, or the vacuum charge, varies when an external potential is switched on. With…
Odd numbers of Dirac points and helical states can exist at edges (surfaces) of two-dimensional (three-dimensional) topological insulators. In the bulk of a one-dimensional lattice (not an edge) with time reversal symmetry, however, a no-go…
Effects of the Dirac sea on the excitation energy of the giant monopole states are investigated in an analytic way within the $\sigma-\omega$ model. The excitation energy is determined by the relativistic Landau-Migdal parameters, $F_0$ and…
We investigate the effective Dirac equation, corrected by merging two scenarios that are expected to emerge towards the quantum gravity scale. Namely, the existence of a minimal length, implemented by the generalized uncertainty principle,…
We discuss free Dirac fermions rotating uniformly inside a cylindrical cavity in the presence of background magnetic field parallel to the cylinder axis. We show that in addition to the known bulk states the system contains massive edge…
This paper begins with a theoretical explanation of why spacetime is discrete. The derivation shows that there exists an elementary length which is essentially Planck's length. We then show how the existence of this length affects time…
Recently, it has been proposed a spacetime noncommutativity that involves spin degrees of freedom, here called "spin noncommutativity". One of the motivations for such a construction is that it preserves Lorentz invariance, which is…
We study massless Dirac fields in a portion of $AdS_3$, where one of the boundaries coincides with the "boundary at infinity" of the Anti-de-Sitter space. We evaluate the vacuum energy arising when the local boundary conditions dictated by…