72 research outputs found
The Dirac field in Taub-NUT background
We investigate the SO(4,1) gauge-invariant theory of the Dirac fermions in
the external field of the Kaluza-Klein monopole, pointing out that the quantum
modes can be recovered from a Klein-Gordon equation analogous to the Schr\"
odinger equation in the Taub-NUT background. Moreover, we show that there is a
large collection of observables that can be directly derived from those of the
scalar theory. These offer many possibilities of choosing complete sets of
commuting operators which determine the quantum modes. In addition there are
some spin- like and Dirac-type operators involving the covariantly constant
Killing-Yano tensors of the hyper-K\" ahler Taub-NUT space. The energy
eigenspinors of the central modes in spherical coordinates are completely
evaluated in explicit, closed form.Comment: 20 pages, latex, no figure
Instanton-Meron Hybrid in the Background of Gravitational Instantons
When it comes to the topological aspects, gravity may have profound effects
even at the level of particle physics despite its negligibly small relative
strength well below the Planck scale. In spite of this intriguing possibility,
relatively little attempt has been made toward the exhibition of this
phenomenon in relevant physical systems. In the present work, perhaps the
simplest and the most straightforward new algorithm for generating solutions to
(anti) self-dual Yang-Mills (YM) equation in the typical gravitational
instanton backgrounds is proposed and then applied to find the solutions
practically in all the gravitational instantons known. Solutions thus obtained
turn out to be some kind of instanton-meron hybrids possessing mixed features
of both. Namely, they are rather exotic type of configurations obeying first
order (anti) self-dual YM equation which are everywhere non-singular and have
finite Euclidean YM actions on one hand while exhibiting meron-like large
distance behavior and carrying generally fractional topological charge values
on the other. Close inspection, however, reveals that the solutions are more
like instantons rather than merons in their generic natures.Comment: 33pages, Revtex, typos correcte
Finite energy/action solutions of Yang-Mills equations on Schwarzschild and deSitter backgrounds for dimension
Physically relevant gauge and gravitational theories can be seen as special
members of hierarchies of more elaborate systems. The Yang-Mills (YM) system is
the first member of a hierarchy of Lagrangians which we will index by ,
and the Einstein-Hilbert (EH) system of general relativity is the first member
of another hierarchy which we index by . In this paper, we study the
classical equations of the YM hierarchy considered in the
background of special geometries (Schwarzschild, deSitter,anti-deSitter) of the
EH hierarchy. Solutions are obtained in various dimensions and lead
to several examples of non-self-dual YM fields. When self-dual
solutions exist in addition. Their action is equal to the Chern-Pontryagin
charge and can be compared with that of the non-self-dual solutions.Comment: LaTeX, 25 pages, 2 figures, new title, minor change
Yang-Mills Solutions on Euclidean Schwarzschild Space
We show that the apparently periodic Charap-Duff Yang-Mills `instantons' in
time-compactified Euclidean Schwarzschild space are actually time independent.
For these solutions, the Yang-Mills potential is constant along the time
direction (no barrier) and therefore, there is no tunneling. We also
demonstrate that the solutions found to date are three dimensional monopoles
and dyons. We conjecture that there are no time-dependent solutions in the
Euclidean Schwarzschild background.Comment: 12 pages, references added, version to appear in PR
Brane inflation and the fine-tuning problem
Brane inflation can provide a promissing framework for solving the
fine-tuning problem in standard inflationary models. The aim of this paper is
to illustrate the mechanism by which this can be achieved. By considering the
supersymmetric two-stage inflation model it is shown that the initial
fine-tuning of the coupling parameter can be considerably relaxed. SubPlanckian
values of the inflaton during inflation can also be obtained.Comment: 04 pages (Revtex
Supersymmetric hybrid inflation in the braneworld scenario
In this paper we reconsider the supersymmetric hybrid inflation in the
context of the braneworld scenario . The observational bounds are satisfied
with an inflationary energy scale , without any
fine-tuning of the coupling parameter, provided that the five-dimensional
Planck scale is . We have also
obtained an upper bound on the the brane tension .Comment: 8 pages (Latex
Dynamical algebra and Dirac quantum modes in Taub-NUT background
The SO(4,1) gauge-invariant theory of the Dirac fermions in the external
field of the Kaluza-Klein monopole is investigated. It is shown that the
discrete quantum modes are governed by reducible representations of the o(4)
dynamical algebra generated by the components of the angular momentum operator
and those of the Runge-Lenz operator of the Dirac theory in Taub-NUT
background. The consequence is that there exist central and axial discrete
modes whose spinors have no separated variables.Comment: 17 pages, latex, no figures. Version to appear in Class.Quantum Gra
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