The Schr\" odinger picture of the Dirac quantum mechanics on spatially flat Robertson-Walker backgrounds

The Schr\" odinger picture of the Dirac quantum mechanics is defined in charts with spatially flat Robertson-Walker metrics and Cartesian coordinates. The main observables of this picture are identified, including the interacting part of the Hamiltonian operator produced by the minimal coupling with the gravitational field. It is shown that in this approach new Dirac quantum modes on de Sitter spacetimes may be found analytically solving the Dirac equation.Comment: 6 pages 0 figure

Geometric models of (d+1)-dimensional relativistic rotating oscillators

Geometric models of quantum relativistic rotating oscillators in arbitrary dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It is shown that these models are analytically solvable, deriving the formulas of the energy levels and corresponding normalized energy eigenfunctions. An important property is that all these models have the same nonrelativistic limit, namely the usual harmonic oscillator.Comment: 7 pages, Late

The leader operators of the (d+1)(d+1)-dimensional relativistic rotating oscillators

The main pairs of leader operators of the quantum models of relativistic rotating oscillators in arbitrary dimensions are derived. To this end one exploits the fact that these models generate P\"{o}schl-Teller radial problems with remarkable properties of supersymmetry and shape invariance.Comment: 11 page

Discrete quantum modes of the Dirac field in AdSd+1AdS_{d+1} backgrounds

It is shown that the free Dirac equation in spherically symmetric static backgrounds of any dimensions can be put in a simple form using a special version of Cartesian gauge in Cartesian coordinates. This is manifestly covariant under the transformations of the isometry group so that the generalized spherical coordinates can be separated in terms of angular spinors like in the flat case, obtaining a pair of radial equations. In this approach the equation of the free field Dirac in $AdS_{d+1}$ backgrounds is analytically solved obtaining the formula of the energy levels and the corresponding normalized eigenspinors.Comment: 18 pages, Latex. Submitted to Phys.Rev.

Approximative analytical solutions of the Dirac equation in Schwarzschild spacetime

Approximative analytic solutions of the Dirac equation in the geometry of Schwarzschild black holes are derived obtaining information about the discrete energy levels and the asymptotic behavior of the energy eigenspinors.Comment: 8 page

Infinite loop superalgebras of the Dirac theory on the Euclidean Taub-NUT space

The Dirac theory in the Euclidean Taub-NUT space gives rise to a large collection of conserved operators associated to genuine or hidden symmetries. They are involved in interesting algebraic structures as dynamical algebras or even infinite-dimensional algebras or superalgebras. One presents here the infinite-dimensional superalgebra specific to the Dirac theory in manifolds carrying the Gross-Perry-Sorkin monopole. It is shown that there exists an infinite-dimensional superalgebra that can be seen as a twisted loop superalgebra.Comment: 16 pages, LaTeX, references adde

SU(n)⊗U(1)cSU(n)\otimes U(1)_c gauge models with spontaneous symmetry breaking

A possible generalization of the technique of the standard model to $SU(n)\otimes U(1)$ gauge models is proposed. A special Higgs mechanism and a new kind of Yukawa couplings in unitary gauge are introduced. These allow us to obtain a general method of deriving boson mass spectrum and coupling coefficients which will be used to find an exact solution of the Pisano-Pleitez three-generation $SU(3)\otimes U(1)$ model. A new anomaly-free one-generation model is briefly discussed.Comment: 41 pages, REVTe