513 research outputs found
Hurewicz fibrations, almost submetries and critical points of smooth maps
We prove that the existence of a Hurewicz fibration between certain spaces
with the homotopy type of a CW-complex implies some topological restrictions on
their universal coverings. This result is used to deduce differentiable and
metric properties of maps between compact Riemannian manifolds under curvature
restrictions
Plane waves from double extended spacetimes
We study exact string backgrounds (WZW models) generated by nonsemisimple
algebras which are obtained as double extensions of generic D--dimensional
semisimple algebras. We prove that a suitable change of coordinates always
exists which reduces these backgrounds to be the product of the nontrivial
background associated to the original algebra and two dimensional Minkowski.
However, under suitable contraction, the algebra reduces to a Nappi--Witten
algebra and the corresponding spacetime geometry, no more factorized, can be
interpreted as the Penrose limit of the original background. For both
configurations we construct D--brane solutions and prove that {\em all} the
branes survive the Penrose limit. Therefore, the limit procedure can be used to
extract informations about Nappi--Witten plane wave backgrounds in arbitrary
dimensions.Comment: 27 pages, no figures, references adde
On the Euler angles for SU(N)
In this paper we reconsider the problem of the Euler parametrization for the
unitary groups. After constructing the generic group element in terms of
generalized angles, we compute the invariant measure on SU(N) and then we
determine the full range of the parameters, using both topological and
geometrical methods. In particular, we show that the given parametrization
realizes the group as a fibration of U(N) over the complex projective
space . This justifies the interpretation of the parameters as
generalized Euler angles.Comment: 16 pages, references adde
Spectral boundary conditions and solitonic solutions in a classical Sellmeier dielectric
Electromagnetic field interactions in a dielectric medium represent a
longstanding field of investigation, both at the classical level and at the
quantum one. We propose a 1+1 dimensional toy-model which consists of an
half-line filling dielectric medium, with the aim to set up a simplified
situation where technicalities related to gauge invariance and, as a
consequence, physics of constrained systems are avoided, and still interesting
features appear. In particular, we simulate the electromagnetic field and the
polarization field by means of two coupled scalar fields ,
respectively, in a Hopfield-like model. We find that, in order to obtain a
physically meaningful behaviour for the model, one has to introduce spectral
boundary conditions depending on the particle spectrum one is dealing with.
This is the first interesting achievement of our analysis. The second relevant
achievement is that, by introducing a nonlinear contribution in the
polarization field , with the aim of mimicking a third order nonlinearity
in a nonlinear dielectric, we obtain solitonic solutions in the Hopfield model
framework, whose classical behaviour is analyzed too.Comment: 12 pages, 1 figur
Pair-production of charged Dirac particles on charged Nariai and ultracold black hole manifolds
Spontaneous loss of charge by charged black holes by means of pair-creation
of charged Dirac particles is considered. We provide three examples of exact
calculations for the spontaneous discharge process for 4D charged black holes
by considering the process on three special non-rotating de Sitter black hole
backgrounds, which allow to bring back the problem to a Kaluza-Klein reduction.
Both the zeta-function approach and the transmission coefficient approach are
taken into account. A comparison between the two methods is also provided, as
well as a comparison with WKB results. In the case of non-zero temperature of
the geometric background, we also discuss thermal effects on the discharge
process.Comment: 27 page
Phi-Psi model for Electrodynamics in dielectric media: exact quantisation in the Heisenberg representation
We investigate the quantization in the Heisenberg representation of a model
which represents a simplification of the Hopfield model for dielectric media,
where the electromagnetic field is replaced by a scalar field and the
role of the polarization field is played by a further scalar field . The
model, which is quadratic in the fields, is still characterized by a nontrivial
physical content, as the physical particles correspond to the polaritons of the
standard Hopfield model of condensed matter physics. Causality is also taken
into account and a discussion of the standard interaction representation is
also considered.Comment: 9 page
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