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

The Dirac particle on de Sitter background

We show that the Dirac equation on de Sitter background can be analytically solved in a special static frame where the energy eigenspinors can be expressed in terms of usual angular spinors known from special relativity, and a pair of radial wave functions.Comment: 9 pages, Late

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

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.

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