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In this article we give sufficient conditions for the generalized Dirac operator to obey the incomplete Huygens principle, as well as necessary and sufficient conditions to obey the Huygens principle by the Dirac operator in the curved spacetime of the Friedmann-Lema^itre-Robertson-Walker models of cosmology.
The operator associated to the angular part of the Dirac equation in the Kerr-Newman background metric is a block operator matrix with bounded diagonal and unbounded off-diagonal entries. The aim of this paper is to establish a variational principle
We present the fundamental solutions for the spin-1/2 fields propagating in the spacetimes with power type expansion/contraction and the fundamental solution of the Cauchy problem for the Dirac equation. The derivation of these fundamental solutions
The equation of the spin-$frac{1}{2}$ particles in the Friedmann-Lema^itre-Robertson-Walker spacetime is investigated. The retarded and advanced fundamental solutions to the Dirac operator and generalized Dirac operator as well as the fundamental sol
We consider a Dirac operator with a dislocation potential on the real line. The dislocation potential is a fixed periodic potential on the negative half-line and the same potential but shifted by real parameter $t$ on the positive half-line. Its spec
We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a source term pr