arXiv subjects

H. J. de Vega

Publications and source records attributed to H. J. de Vega.

At least 145 records · Page 8Linked to original sources

arXiv1996

Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes

The string propagation equations in axisymmetric spacetimes are exactly solved by quadratures for a planetoid Ansatz. This is a straight non-oscillating string, radially disposed, which rotates uniformly around the symmetry axis of the spacetime. In Schwarzschild black holes, the string stays outside the horizon pointing towards the origin. In de Sitter spacetime the planetoid rotates around its center. We quantize semiclassically these solutions and analyze the spin/(mass$^2$) (Regge) relation for the planetoids, which turns out to be non-linear.

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arXiv1996

Evolution of Inhomogeneous Condensates after Phase Transitions

Using the O(4) linear $σ$ model, we address the topic of non-equilibrium relaxation of an inhomogeneous initial configuration due to quantum and thermal fluctuations. The space-time evolution of an inhomogeneous fluctuation of the condensate in the isoscalar channel decaying via the emission of pions in the medium is studied within the context of disoriented chiral condensates. We use out of equilibrium closed time path methods in field theory combined with the amplitude expansion. We give explicit expressions for the asymptotic space-time evolution of an initial inhomogeneous configuration including the contribution of thresholds at zero and non-zero temperature. At non-zero temperature we find new relaxational processes due to thermal cuts that have no counterpart in the homogeneous case. Within the one-loop approximation, we find that the space time evolution of such inhomogeneous configuration out of equilibrium is effectively described in terms of a rapidity dependent temperature $T(\vartheta)=T/\cosh[\vartheta]$ as well as a rapidity dependent decay rate $Γ(\vartheta, T(\vartheta))$. This rate is to be interpreted as the production minus absorption rate of pions in the medium and approaches the zero temperature value at large rapidities. An initial configuration localized on a bounded region spreads and decays in spherical waves with slower relaxational dynamics at large rapidity.

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arXiv1996

Quantum Bosonic String Energy-Momentum Tensor in Minkowski Space-Time

The quantum energy-momentum tensor ${\hat T}^{μν}(x)$ is computed for strings in Minkowski space-time. We compute its expectation value for different physical string states both for open and closed bosonic strings. The states considered are described by normalizable wave-packets in the center of mass coordinates. We find in particular that ${\hat T}^{μν}(x)$ is {\bf finite} which could imply that the classical divergence that occurs in string theory as we approach the string position is removed at the quantum level as the string position is smeared out by quantum fluctuations. For massive string states the expectation value of ${\hat T}^{μν}(x)$ vanishes at leading order (genus zero). For massless string states it has a non-vanishing value which we explicitly compute and analyze for both spherically and cylindrically symmetric wave packets. The energy-momentum tensor components propagate outwards as a massless lump peaked at $ r = t $.

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arXiv1995

Lectures on String Theory in Curved Spacetimes

Recent progress on string theory in curved spacetimes is reviewed. The string dynamics in cosmological and black hole spacetimes is investigated.The methods to solve the string equations of motion in curved spacetimes are described.That is, the perturbation approach, the null approach, the $τ$-expansion, and the construction of global solutions.The behaviour of strings in FRW and inflatio- nary spacetimes is obtained from the various types of string solutions. Three different types of behaviour appear:{\bf unstable, dual} to unstable and {\bf stable}.For the unstable strings, the energy and size grow proportional to $R$ for large scale factors $R \to \infty$. For the dual to unstable strings, the energy and size blow up for R\to 0 as 1/R. For stable strings, the energy and size are bounded. (In Minkowski, all solutions are of the stable type). The self-consistent solution to the Einstein equations for string dominated universes is reviewed. The energy-momentum tensor for a gas of strings is taken as source and from the above behaviours the string equation of state is {\bf derived}. The self-consistent string solution exhibits realistic matter dominated behaviour for large times and radiation dominated behaviour for early times. We report on the {\bf exact integrability} of the string dynamics in de Sitter spacetime that allows to systematically find {\bf exact} string solutions by soliton methods. {\bf Multistring solutions} are a new feature in curved spacetimes. That is, a single world-sheet simultaneously describes many different and independent strings. This phenomenon has no analogue in flat spacetime and follows from the coupling of the strings with the geometry. Finally, the string dynamics next and inside a Schwarzschild black hole is analyzed and their physical properties discussed.

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arXiv1995

New Aspects of Reheating

The reheating stage in post-inflationary cosmologies is reanalyzed. New techniques from non-equilibrium quantum field theory allow a consistent derivation of the equation of motion including the non-linearity of the dynamics. These offer a rationale for the elementary theory of reheating based on single particle decay which is seen to be valid only in the linear regime of coherent oscillations of the scalar field. A new non-perturbative mechanism of induced amplification of quantum fluctuations is introduced and studied in detail, both analytically and numerically. This is a non-linear mechanism that is typically a far more efficient way of transfering energy out of the zero mode and into production of lighter particles than single particle decay. Thermalization is discussed and we estimate the reheating temperature to be of the order of the inflaton mass, thus providing a potential solution to the Polonyi and moduli problems.

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arXiv1995

Reheating and Thermalization, Linear Vs. Non-Linear Relaxation

We consider the case of a scalar field, the inflaton, coupled to both lighter scalars and fermions, and the study the relaxation of the inflaton via particle production in both the linear and non-linear regimes. This has an immediate application to the reheating problem in inflationary universe models. The linear regime analysis offers a rationale for the standard approach to the reheating problem, but we make a distinction between relaxation and thermalization. We find that particle production when the inflaton starts in the {\it non-linear} region is typically a far more efficient way of transfering energy out of the inflaton zero mode and into the quanta of the lighter scalar than single particle decay. For the non-linear regime we take into account self-consistently the evolution of the expectation value of the inflaton field coupled to the evolution of the quantum fluctuations. An exhaustive numerical analysis reveals that the distribution of produced particles is far from thermal, and the effect of open channels. In the fermionic case, Pauli blocking begins to hinder the transfer of energy into the fermion modes very early on in the evolution of the inflaton. We examine the implications of our results to the question of how to calculate the reheating temperature of the universe after inflation.

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arXiv1995

Strings Next To and Inside Black Holes

The string equations of motion and constraints are solved near the horizon and near the singularity of a Schwarzschild black hole. In a conformal gauge such that $τ= 0$ ($τ$ = worldsheet time coordinate) corresponds to the horizon ($r=1$) or to the black hole singularity ($r=0$), the string coordinates express in power series in $τ$ near the horizon and in power series in $τ^{1/5}$ around $r=0$. We compute the string invariant size and the string energy-momentum tensor. Near the horizon both are finite and analytic. Near the black hole singularity, the string size, the string energy and the transverse pressures (in the angular directions) tend to infinity as $r^{-1}$. To leading order near $r=0$, the string behaves as two dimensional radiation. This two spatial dimensions are describing the $S^2$ sphere in the Schwarzschild manifold.

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arXiv1995

STRING THEORY IN COSMOLOGICAL SPACETIMES

Progress on string theory in curved spacetimes since 1992 are reviewed. After a short introduction on strings in Minkowski and curved spacetimes, we focus on strings in cosmological spacetimes. The classical behaviour of strings in FRW and inflationary spacetimes is now understood in a large extent from various types of explicit string solutions. Three different types of behaviour appear in cosmological spacetimes: {\bf unstable, dual} to unstable and {\bf stable}. For the unstable strings, the energy and size grow for large scale factors $R \to \infty$, proportional to $R$. For the dual to unstable strings, the energy and size blow up for $R\to 0$ as $1/R$. For stable strings, the energy and proper size are bounded. (In Minkowski spacetime, all string solutions are of the stable type).Recent progress on self-consistent solutions to the Einstein equations for string dominated universes is reviewed. The energy-momentum tensor for a gas of strings is then considered as source of the spacetime geometry and from the above string behaviours the string equation of state is determined. The self-consistent string solution exhibits the realistic matter dominated behaviour $R \sim (X^0)^{2/3}\; $ for large times and the radiation dominated behaviour $R \sim (X^0)^{1/2}\;$ for early times. Finally, we report on the exact integrability of the string equations plus the constraints in de Sitter spacetime that allows to systematically find {\bf exact} string solutions by soliton methods and the multistring solutions. {\bf Multistring solutions} are a new feature in curved spacetimes. That is, a single world-sheet simultaneously describes many different and independent strings. This phenomenon has no analogue in flat spacetime and follows to the coupling of the strings with the geometry.

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arXiv1995

STRINGS IN COSMOLOGICAL SPACETIMES AND THEIR BACK-REACTION

This is a short review on strings in curved spacetimes. We start by recalling the classical and quantum string behaviour in singular plane waves backgrounds. We then report on the string behaviour in cosmological spacetimes (FRW, de Sitter, power inflation) which is by now largerly understood. Recent progress on self-consistent solutions to the Einstein equations for string dominated universes is reviewed. The energy-momentum tensor for a gas of strings is considered as source of the spacetime geometry. The string equation of state is determined from the behaviour of the explicit string solutions. This yields a self-consistent cosmological solution exhibiting realistic matter dominated behaviour $ R \sim (T)^{2/3}\; $ for large times and radiation dominated behaviour $ R \sim (T)^{1/2}\; $ for early times. Inflation in the string theory context is discussed.

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arXiv1995

MULTISTRING SOLUTIONS IN INFLATIONARY SPACETIMES

Multistring solutions of the string equations of motion are found for inflationary spacetimes with expansion factor $R(η)\propto η^k$ for any $k<0$ and $η$ conformal time. If $0>k>-1$ only two-string solutions can be found within our ansatz, whereas for $k=-1-1/n$, with $n=1,2,\ldots$, multistring solutions exist with an infinite number of strings [In the special case $k=-2$ we recover de Sitter spacetime where multistring solutions were first found].

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arXiv1995

Reheating the Post Inflationary Universe

We consider the non-equilibrium evolution of the inflaton field coupled to both lighter scalars and fermions. The dissipational dynamics of this field is studied and found to be quite different than that believed in inflationary models. In particular, the damping time scale for the expectation value of the zero momentum mode of the inflaton can be much shorter than that given by the single particle decay rate when the inflaton amplitudes are large, as in chaotic inflation scenarios. We find that the reheating temperature may depart considerably from the usual estimates.

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arXiv1995

Circular Strings and Multi-Strings in de Sitter and Anti de Sitter Spacetimes

The exact general solution of circular strings in $2+1$ dimensional de Sitter spacetime is described completely in terms of elliptic functions. The novel feature here is that one single world-sheet generically describes {\it infinitely many} (different and independent) strings. This has no analogue in flat spacetime. The circular strings are either oscillating ("stable") or indefinitely expanding ("unstable"). We then compute the {\it exact} equation of state of circular strings in the $2+1$ dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting and expanding) strings. We finally perform a semi-classical quantization of the oscillating circular strings. We find the mass formula $α'm^2_{\mbox{dS}}\approx 4n-5H^2α'n^2,\;(n\in N_0),$ and a {\it finite} number of states $N_{\mbox{dS}}\approx 0.34/(H^2α')$ in de Sitter spacetime; $m^2_{\mbox{AdS}}\approx H^2n^2$ (large $n\in N$) and $N_{\mbox{AdS}}=\infty$ in anti de Sitter spacetime. The level spacing grows with $n$ in AdS spacetime, while is approximately constant (although smaller than in Minkowski spacetime and slightly decreasing) in dS spacetime.

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arXiv1995

CLASSICAL SPLITTING OF FUNDAMENTAL STRINGS

We find exact solutions of the string equations of motion and constraints describing the {\em classical}\ splitting of a string into two. We show that for the same Cauchy data, the strings that split have {\bf smaller} action than the string without splitting. This phenomenon is already present in flat space-time. The mass, energy and momentum carried out by the strings are computed. We show that the splitting solution describes a natural decay process of one string of mass $M$ into two strings with a smaller total mass and some kinetic energy. The standard non-splitting solution is contained as a particular case. We also describe the splitting of a closed string in the background of a singular gravitational plane wave, and show how the presence of the strong gravitational field increases (and amplifies by an overall factor) the negative difference between the action of the splitting and non-splitting solutions.

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arXiv1994

Unified Approach to Thermodynamic Bethe Ansatz and Finite Size Corrections for Lattice Models and Field Theories

We present a unified approach to the Thermodynamic Bethe Ansatz (TBA) for magnetic chains and field theories that includes the finite size (and zero temperature) calculations for lattice BA models. In all cases, the free energy follows by quadratures from the solution of a {\bf single} non-linear integral equation (NLIE). [A system of NLIE appears for nested BA]. We derive the NLIE for: a) the six-vertex model with twisted boundary conditions; b) the XXZ chain in an external magnetic field $h_z$ and c) the sine-Gordon-massive Thirring model (sG-mT) in a periodic box of size $\b \equiv 1/T $ using the light-cone approach. This NLIE is solved by iteration in one regime (high $T$ in the XXZ chain and low $T$ in the sG-mT model). In the opposite (conformal) regime, the leading behaviors are obtained in closed form. Higher corrections can be derived from the Riemann-Hilbert form of the NLIE that we present.

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arXiv1994

String Quantization in Curved Spacetimes: Null String Approach

We study quantum strings in strong gravitational fields. The relevant small parameter is $g=R_c{\sqrt T_0}$, where $R_c$ is the curvature of the spacetime and $T_0$ is the string tension. Within our systematic expansion we obtain to zeroth order the null string (string with zero tension), while the first order correction incorporates the string dynamics. We apply our formalism to quantum null strings in de Sitter spacetime. After a reparametrization of the world-sheet coordinates, the equations of motion are simplified. The quantum algebra generated by the constraints is considered, ordering the momentum operators to the right of the coordinate operators. No critical dimension appears. It is anticipated however that the conformal anomaly will appear when the first order corrections proportional to $T_0$, are introduced.

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arXiv1994

Non-Equilibrium Dynamics of Phase Transitions: From the Early Universe to Chiral Condensates

In this brief review we introduce the methods of quantum field theory out of equilibrium and study the non-equilibrium aspects of phase transitions. Specifically we critically study the picture of the ``slow-roll'' phase transition in the new inflationary models, we show that the instabilities that are the hallmark of the phase transition, that is the formation of correlated domains, dramatically change this picture. We analyze in detail the dynamics of phase separation in strongly supercooled phase transitions in Minkowski space. We argue that this is typically the situation in weakly coupled scalar theories. The effective evolution equations for the expectation value and the fluctuations of an inflaton field in a FRW cosmology are derived both in the loop expansion and in a self-consistent non-perturbative scheme. Finally we use these non-equilibrium techniques and concepts to study the influence of quantum and thermal fluctuations on the dynamics of a proposed mechanism for the formation of disoriented chiral condensates during a rapid phase transition out of equilibrium. This last topic may prove to be experimentally relevant at present accelerator energies. To appear in the Proceedings of the `2nd. Journée Cosmologie', Observatoire de Paris, 2-4, June 1994. H J de Vega and N. Sánchez, Editors, World Scientific.

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arXiv1994

Semi-Classical Quantization of Circular Strings in De Sitter and Anti De Sitter Spacetimes

We compute the {\it exact} equation of state of circular strings in the (2+1) dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting and expanding) strings. The string equation of state has the perfect fluid form $P=(γ-1)E,$ with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient $γ$ depending on the elliptic modulus. We semi-classically quantize the oscillating circular strings. The string mass is $m=\sqrt{C}/(πHα'),\;C$ being the Casimir operator, $C=-L_{μν}L^{μν},$ of the $O(3,1)$-dS [$O(2,2)$-AdS] group, and $H$ is the Hubble constant. We find $α'm^2_{\mbox{dS}}\approx 5.9n,\;(n\in N_0),$ and a {\it finite} number of states $N_{\mbox{dS}}\approx 0.17/(H^2α')$ in de Sitter spacetime; $m^2_{\mbox{AdS}}\approx 4H^2n^2$ (large $n\in N_0$) and $N_{\mbox{AdS}}=\infty$ in anti de Sitter spacetime. The level spacing grows with $n$ in AdS spacetime, while is approximately constant (although larger than in Minkowski spacetime) in dS spacetime. The massive states in dS spacetime decay through tunnel effect and the semi-classical decay probability is computed. The semi-classical quantization of {\it exact} (circular) strings and the canonical quantization of generic string perturbations around the string center of mass strongly agree.

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arXiv1994

The Highest Weight Property for the $SU_{q}(n)$ Invariant Spin Chains

The $SU_{q}(n)$ generators are obtained as large spectral parameter limit of the Yang-Baxter operators in the integrable $SU_{q}(n)$ invariant vertex model. The commutation relations, including Serre relations, are obtained as limits of the Yang-Baxter equations. The recently found eigenvectors of the $SU_{q}(n)$ invariant spin chains are shown to be Highest Weight vectors of the corresponding quantum group.

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