The de Broglie-Bohm causal theory of quantum mechanics is applied to the hydrogen atom in the fully spin-dependent and relativistic framework of the Dirac equation, and in the nonrelativistic but spin-dependent framework of the Pauli equation. Eigenstates are chosen which are simultaneous eigenstates of the energy H , total angular momentum M , and z component of the total angular momentum Mz. ...

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...

We calculate all symmetries of the Dirac-Pauli equation in twodimensional and three-dimensional Euclidean space. Further, we use our results for an investigation of the issue of zero mode degeneracy. email: [email protected] email: [email protected]

One of the most important reactions of the URCA that lead to the cooling of a neutron star, is neutron beta-decay ( ). In this research, the energy spectra and wave functions of massive fermions taking into account the Anomalous Magnetic Moment (AMM) in the presence of a strong changed magnetic field are calculated. For this purpose, the Dirac-Pauli equation for charged and neutral fermions is ...

Herein, the Dirac equation is compared with the KleinGordon equation. In contrast to the Dirac case, it is proved that the Klein-Gordon equation has difficulties with the Hamiltonian differential operator of relativistic quantum mechanics and with the definition of an inner product of wave functions, which is a requirement for a construction of a Hilbert space. An added discussion of the Pauli-...

We present a new step in the foundation of quantum field theory with the tools of scale relativity. Previously, quantum motion equations (Schrödinger, Klein–Gordon, Dirac, Pauli) have been derived as geodesic equations written with a quantum-covariant derivative operator. Then, the nature of gauge transformations, of gauge fields and of conserved charges have been given a geometric meaning in t...

In this paper we demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasiexactly solvable systems. Electric field configurations permitting quasi-exact solvability of the system based on the sl(2) symmetry are discussed separately in spherical, cylindrical, and Cartesian coordinates. Some exactly ...

In quantum information context, the groups generated by Pauli spin matrices, and Dirac gamma matrices, are known as the single qubit Pauli group P , and two-qubit Pauli group P2, respectively. It has been found [M. Socolovsky, Int. J. Theor. Phys. 43, 1941 (2004)] that the CPT group of the Dirac equation is isomorphic to P . One introduces a two-qubit entangling orthogonal matrix S basically re...

A generalization of the pseudoclassical action of a spinning particle in the presence of an anomalous magnetic momentum is given. The action is written in reparametrization and supergauge invariant form. The Dirac quantization, based on the Hamiltonian analyses of the model, leads to the Dirac-Pauli equation for a particle with an anomalous magnetic momentum in an external electromagnetic field...