In this paper we give a mathematically rigorous analysis of the Klein paradox in the many-particle formulation of the Dirac theory. This paradox was meant as an example demonstrating the negative energy problems of the single particle Dirac equation. However, we show that this problem does not disappear in the second quantized version of the Dirac theory. It corresponds with a situation which c...

We study spin-flavor oscillations of Dirac neutrinos with mixing and having non-zero matrix of magnetic moments in magnetic fields of various configurations. We discuss constant transversal and twisting magnetic fields. To describe the dynamics of Dirac neutrinos we use relativistic quantum mechanics approach based on the exact solutions to the Dirac-Pauli equation in an external electromagneti...

It is proven that a recently derived simple configuration-space wave equation for two spin-l/2 particles is equivalent to the Breit equation and to the Salpeter equation in first order perturbation theory. The wave equation is based on a simple quasipotential approximation. The potential in the equation is given by the Blankenbecler-Sugar correction series. The proof holds for an arbitrary comb...

In this paper, model reference neural network structure is used as a controller for vibration suppression of the Euler–Bernoulli beam under the excitation of moving mass travelling along a vibrating path. The non-dimensional equation of motion the beam acted upon by a moving mass is achieved.  A Dirac-delta function is used to describe the position of the moving mass along the beam and its iner...

We consider the Cauchy problem for the massive Dirac equation in the non-extreme Kerr-Newman geometry outside the event horizon. We derive an integral representation for the Dirac propagator involving the solutions of the ODEs which arise in Chandrasekhar's separation of variables. It is proved that for initial data in L ∞ loc near the event horizon with L 2 decay at infinity, the probability o...

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 transformations corresponding to isometries that give rise to conserved quantities according to the Noether theorem. With their help the plane wave spinor solutions o...

We consider the Cauchy problem for the massive Dirac equation in the non-extreme Kerr-Newman geometry outside the event horizon. We derive an integral representation for the Dirac propagator involving the solutions of the ODEs which arise in Chandrasekhar's separation of variables. It is proved that for initial data in L ∞ loc near the event horizon with L 2 decay at infinity, the probability o...

Maxwell equation ∂F = 0 for F ∈ sec ∧2 M ⊂ sec Cl(M), where Cl(M) is the Clifford bundle of differential forms, have subluminal and superluminal solutions characterized by F 2 6= 0. We can write F = ψγ21ψ̃ where ψ ∈ sec Cl(M). We can show that ψ satisfies a non linear DiracHestenes Equation (NLDHE). Under reasonable assumptions we can reduce the NLDHE to the linear Dirac-Hestenes Equation (DHE)....

The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr–Newman geometry, for smooth initial data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays in L∞loc at least at the rate t−5/6. For generic initial data, this rate of decay is sharp. We derive a formula for the probabilityp that the Dira...

We consider the Cauchy problem for the massive Dirac equation in the non-extreme Kerr-Newman geometry outside the event horizon. We derive an integral representation for the Dirac propagator involving the solutions of the ODEs which arise in Chandrasekhar’s separation of variables. It is proved that for initial data in L∞ loc near the event horizon with L decay at infinity, the probability of t...