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 $SU(N+1)$ as a fibration of U(N) over the complex projective space $\mathbb{CP}^n$. 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 $\phi$,$\psi$ 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 $\psi$, 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 $\phi$ and the role of the polarization field is played by a further scalar field $\psi$. 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