Dirac Equation In Spacetime Research Articles

Huygens' principle for the Dirac equation in spacetime of non-constant curvature

In this article we give sufficient and necessary conditions for the validity of the Huygens' principle for the Dirac equation in the non-constant curvature spacetime of the Friedmann-Lemaître-Robertson-Walker models of cosmology. The Huygens' principle discussed for the equation of a field with mass m=0 as well as a massive spin-12 field undergoing a red shift of its wavelength as the universe expands.

Massless fermions on static general prolate metrics and their Heun solutions

Employing a pseudo-orthonormal coordinate-free approach, we write down the Dirac equation in spacetimes with static general prolate metrics. As examples, we consider the electrically charged C-metric, the vacuum C-metric, the Reissner–Nordström and Schwarzschild spacetimes and the BBMB black hole and show that the solutions to the Dirac equations for particles in these spacetimes can be derived in terms of Heun’s general functions and their confluent and double confluent forms. By imposing boundary conditions to the radial solutions, the so-called resonant frequencies are obtained.

Separation of the Dirac equation in the (3 + 1)-dimensional constant curvature black hole background and its solution

The behavior of spin-half particles is discussed in the (3 + 1)-dimensional constant curvature black hole (CCBH) spacetime. We use Schwarzschild-like coordinates, valid outside the black hole event horizon. The constant time surfaces corresponding to the timelike Killing vector are degenerate at the black hole event horizon and also along an axis. We write down the Dirac equation in this spacetime using the Newman–Penrose formalism which is not easily separable unlike that in the Kerr metric. However, with a particular choice of basis system the equation is separable and we obtain the solutions. We discuss the structural difference in the Dirac equation in the CCBH spacetime with that in the Kerr geometry, due to a difference in the corresponding spacetime metrices the resulting complexity arose in separation in the earlier case.

Particle and Antiparticle sectors in DSR1 and -Minkowski space-time

In this paper we explore the problem of antiparticles in DSR1 and $\kappa$-Minkowski space-time following three different approaches inspired by the Lorentz invariant case: a) the dispersion relation, b) the Dirac equation in space-time and c) the Dirac equation in momentum space. We find that it is possible to define a map $S_{dsr}$ which gives the antiparticle sector from the negative frequency solutions of the wave equation. In $\kappa$-Poincar\'e, the corresponding map $S_{kp}$ is the antipodal mapping, which is different from $S_{dsr}$. The difference is related to the composition law, which is crucial to define the multiparticle sector of the theory. This discussion permits to show that the energy of the antiparticle in DSR is the positive root of the dispersion relation, which is consistent with phenomenological approaches.