arXiv subjects

E. Abdalla

Publications and source records attributed to E. Abdalla.

At least 55 records · Page 3Linked to original sources

arXiv2004

Field propagation in the Schwarzschild-de Sitter black hole

We present an exhaustive analysis of scalar, electromagnetic and gravitational perturbations in the background of a Schwarzchild-de Sitter spacetime. The field propagation is considered by means of a semi-analytical (WKB) approach and two numerical schemes: the characteristic and general initial value integrations. The results are compared near the extreme regime, and a unifying picture is established for the dynamics of different spin fields. Although some of the results just confirm usual expectations, a few surprises turn out to appear, as the dependence on the non-characteristic initial conditions of the non-vanishing asymptotic value for l=0 mode scalar fields.

gr-qc↗

arXiv2003

Area Quantization in Quasi-Extreme Black Holes

We consider quasi-extreme Kerr and quasi-extreme Schwarzschild-de Sitter black holes. From the known analytical expressions obtained for their quasi-normal modes frequencies, we suggest an area quantization prescription for those objects.

gr-qc↗

arXiv2002

Support of dS/CFT correspondence from space-time perturbations

We analyse the spectrum of perturbations of the de Sitter space on the one hand, while on the other hand we compute the location of the poles in the Conformal Field Theory (CFT) propagator at the border. The coincidence is striking, supporting a dS/CFT correspondence. We show that the spectrum of thermal excitations of the CFT at the past boundary $I^{-}$ together with that spectrum at the future boundary $I^{+}$ is contained in the quasi-normal mode spectrum of the de Sitter space in the bulk.

hep-th↗

arXiv2002

Evolving of a massless scalar field in Reissner--Nordström Anti--de Sitter spacetimes

We investigate the evolution of a scalar field propagating in Reissner--Nordström Anti--de Sitter spacetime. Due to the characteristic of spacetime geometry, the radiative tails associated with a massless scalar field propagation have an oscillatory exponential decay. The object--picture of the quasinormal ringing has also been obtained. For small charges, the approach to thermal equilibrium is faster for larger charges. However, after the black hole charge reaches a critical value, we get the opposite behavior for the imaginary frequencies of the quasinormal modes. Some possible explanations concerning the wiggle of the imaginary frequencies have been given. The picture of the quasinormal modes depending on the multipole index has also been illustrated.

hep-th↗

arXiv1998

Scale-invariant Perturbation of the Friedmann Universe

We use de Vaucouleurs' power-law density-distance relation, to study a hierarchical perturbation of the Friedmann universe. We solve the Einstein equation and obtain the density contrast and the amplification factor for the perturbation. It is shown that, scale-invariant inhomogeneities decay in Einstein-de-Sitter universe. On the contrary, in an open universe, the inhomogeneities grow. For low values of $Ω$, amplification peaks sharply and the fluctuations can grow by up to a factor of $10^{13}$ from the recombination to the present time. Our analysis of the closed universe further confirms that, unlike the common belief that perturbations grow faster with increasing $Ω$, scale-invariant perturbations amplify with decreasing $Ω$. This result is consistent with the very low density expected for a hierarchical universe.

astro-ph↗

arXiv1998

Numerical study of the decay amplitudes in two dimensional QCD

After presenting a survey of theoretical results concerning the structure of two-dimensional QCD, we present a numerical study related to the mass eigenstates and the decay amplitudes of higher mesonic states. We discuss in detail the fate of important dynamical points such as stability of the spectrum and the problem of screening versus confinement in this context. We point out differences in the large distance behaviour of the potential, which can be responsible for the question of stability of the spectrum, as well as whether it is finite.

hep-th↗

arXiv1998

Screening in three-dimensional QED with arbitrary fermion mass

We compute the quark--antiquark potential in three dimensional massive Quantum Electrodynamics for arbitrary fermion mass. The result indicates that screening prevails for any quark masses, contrary to the classical expectations, generalizing our previous result obtained for large masses. We also test the validity of several approximation schemes using a detailed numerical analysis. The classical result is still reproduced for small separation of the quarks.

hep-th↗

arXiv1998

A Dynamical Approach to a Self-similar Universe

We write a non-relativistic Lagrangian for a hierarchical universe. The equations of motion are solved numerically and the evolution of the fractal dimension is obtained for different initial conditions. We show that our model is homogeneous at the time of the last scattering, but evolves into a self-similar universe with a remarkably constant fractal dimension. We also show that the Hubble law is implied by this model and make an estimate for the age of the universe.

astro-ph↗

arXiv1998

Quantization of the multidimensional rotor

We reconsider the problem of quantising a particle on the $D$-dimensional sphere. Adopting a Lagrangian method of reducing the degrees of freedom, the quantum Hamiltonian is found to be the usual Schrödinger operator without any boundary term. The equivalence with the Dirac Hamiltonian approach is demonstrated, either in the cartesian or in the curvilinear basis. We also briefly comment on the path integral approach.

quant-ph↗

arXiv1997

Screening in three-dimensional QED

We compute the quark-antiquark potential in three dimensional massive Quantum Electrodynamics. The result indicates that screening prevails for large quark masses, contrary to the classical expectations. The classical result is reproduced for small separation of the quarks.

hep-th↗

arXiv1997

Two-dimensional Quantum Field Theory, examples and applications

The main principles of two-dimensional quantum field theories, in particular two-dimensional QCD and gravity are reviewed. We study non-perturbative aspects of these theories which make them particularly valuable for testing ideas of four-dimensional quantum field theory. The dynamics of confinement and theta vacuum are explained by using the non-perturbative methods developed in two dimensions. We describe in detail how the effective action of string theory in non-critical dimensions can be represented by Liouville gravity. By comparing the helicity amplitudes in four-dimensional QCD to those of integrable self-dual Yang-Mills theory, we extract a four dimensional version of two dimensional integrability.

hep-th↗

arXiv1996

Operator solutions of two-dimensional chiral gauge theories

The exact operator solutions of two-dimensional anomaly-free chiral abelian gauge theories are obtained. We show that anomaly-cancellation conditions arise as consistency requirements of these solutions. For a certain class of flavour symmetries, fermion condensates are constructed. These are shown to violate the fermion-number conservation rule. The models are extended to include massive fermions. We propose a bosonised lagrangian for the massive theory and verify that it complies with the Gupta-Bleuler condition.

hep-th↗

arXiv1996

Screening in Two-dimensional QCD

We discuss the issue of screening and confinement of external colour charges in bosonised two-dimensional quantum chromodynamics. Our computation relies on the static solutions of the semi-classical equations of motion. The significance of the different representations of the matter field is explicitly studied. We arrive at the conclusion that the screening phase prevails, even in the presence of a small mass term for the fermions. To confirm this result further, we outline the construction of operators corresponding to screened quarks.

hep-th↗

arXiv1995

Massive Two-Dimensional Quantum Chromodynamics

In this work we study the zero-charge sector of massive two-dimensional Quantum Chromodynamics in the decoupled formulation. We find that some general features of the massless theory, concerning the constraints and the right- and left-moving character of the corresponding BRST currents, survive in the massive case. The implications for the integrability properties previously valid in the massless case, and the structure of the Hilbert space are discussed.

hep-th↗

arXiv1995

Three-dimensional quantum electrodynamics as an effective interaction

We obtain a Quantum Electrodynamics in 2+1 dimensions by applying a Kaluza--Klein type method of dimensional reduction to Quantum Electrodynamics in 3+1 dimensions rendering the model more realistic to application in solid-state systems, invariant under translations in one direction. We show that the model obtained leads to an effective action exhibiting an interesting phase structure and that the generated Chern--Simons term survives only in the broken phase.

hep-th↗

arXiv1995

Towards a solution of two dimensional QCD

Using the well-known result for the fermionic determinant in terms of a WZW theory, we write QCD$_2$ in bosonized form. After some manipulations we give two versions of the theory, where it is factorized as a product of the conformally invariant WZW models, ghost terms, and a WZW action perturbed off criticality. We first prove that the latter is an integrable model. Furthermore, as a consequence of the BRST analysis, there are several constraints. Second-class constraints also show up. Using the integrability condition we find higher conservation laws, their action on the asymptotic states, and we propose an exact $S$-matrix for the physical excitations. The vacuum structure is analysed, and we prove that a finite number of different vacua exist. An outline of possible generalizations of the procedure is given.

hep-th↗

arXiv1995

Gravitational Interactions of integrable models

We couple non-linear $σ$-models to Liouville gravity, showing that integrability properties of symmetric space models still hold for the matter sector. Using similar arguments for the fermionic counterpart, namely Gross--Neveu-type models, we verify that such conclusions must also hold for them, as recently suggested.

hep-th↗

arXiv1995

BRST Cohomology and Vacuum Structure of Two-Dimensional Chromodynamics

Using a formulation of QCD_2 as a perturbed conformally invariant theory involving fermions, ghosts, as well as positive and negative level Wess-Zumino-Witten fields, we show that the BRST conditions become restrictions on the conformally invariant sector, as described by a G/G topological theory. By solving the corresponding cohomology problem we are led to a finite set of vacua. For G=SU(2) these vacua are two-fold degenerate.

hep-th↗