109 research outputs found
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 -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 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 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
gauge models with spontaneous symmetry breaking
A possible generalization of the technique of the standard model to
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 model. A new anomaly-free one-generation
model is briefly discussed.Comment: 41 pages, REVTe
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