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AbstractAbstract

[en] Non-singular two and three dimensional string cosmologies are constructed using the exact conformal field theories corresponding to SO(2,1)/SO(1,1) and SO(2,2)/SO(2,1). All semi-classical curvature singularities are canceled in the exact theories for both of these cosets, but some new quantum curvature singularities emerge. However, considering different patches of the global manifolds, allows the construction of non-singular space-times with cosmological interpretation. In both two and three dimensions, we construct non-singular oscillating cosmologies, non-singular expanding and inflationary cosmologies including a de Sitter (exponential) stage with positive scalar curvature as well as non-singular contracting and deflationary cosmologies. Similarities between the two and three dimensional cases suggest a general picture for higher dimensional coset cosmologies: Anisotropy seems to be a generic unavoidable feature, cosmological singularities are generically avoided and it is possible to construct non-singular cosmologies where some spatial dimensions are experiencing inflation while the others experience deflation

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International conference on supersymmetry and quantum field theory; Kharkov (Ukraine); 25-29 Jul 2000; S0920563201015572; Copyright (c) 2001 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

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Nuclear Physics. B, Proceedings Supplements; ISSN 0920-5632; ; CODEN NPBSE7; v. 102-103(1-3); p. 201-208

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[en] Higher-order corrections to the soliton mass in two-dimensional scalar field theories, are studied. It is shown that the second quantum correction (two-loop graphs) to the soliton mass (Msub(s)) is finite provided one orders correctly the non-commuting operators in the effective hamiltonian. That is, the vacuum sector UV counterterm suffices to eliminate the ultraviolet and infinite volume divergences of the one-soliton sector. The finite part of the second quantum correction to Msub(s) in the sine-Gordon model is explicitly evaluated. It is found that the ratio of the soliton mass to the meson mass is the same in this perturbative calculation, as in the semiclassical one by Dashen, Hasslacher and Neveu, up to two-loop contributions. (Auth.)

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Nuclear Physics. B; v. 115(3); p. 411-428

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Vega, H.J. de; Sanchez, N., E-mail: devega@lpthe.jussieu.fr

AbstractAbstract

[en] We complete our study of the self-gravitating gas by computing the fluctuations around the saddle point solution for the three statistical ensembles (grand canonical, canonical and microcanonical). Although the saddle point is the same for the three ensembles, the fluctuations change from one ensemble to the other. The zeroes of the small fluctuations determinant determine the position of the critical points for each ensemble. This yields the domains of validity of the mean field approach. Only the S-wave determinant exhibits critical points. Closed formulae for the S- and P-wave determinants of fluctuations are derived. The local properties of the self-gravitating gas in thermodynamic equilibrium are studied in detail. The pressure, energy density, particle density and speed of sound are computed and analyzed as functions of the position. The equation of state turns out to be locally p(r→ )=Tρ

_{V}(r→ ) as for the ideal gas. Starting from the partition function of the self-gravitating gas, we prove in this microscopic calculation that the hydrostatic description yielding locally the ideal gas equation of state is exact in the N=∞ limit. The dilute nature of the thermodynamic limit (N∼L→∞ with N/L fixed) together with the long range nature of the gravitational forces play a crucial role in obtaining such ideal gas equation. The self-gravitating gas being inhomogeneous, we have PV/[NT]=f(η)≤1 for any finite volume V. The inhomogeneous particle distribution in the ground state suggests a fractal distribution with Haussdorf dimension D, D is slowly decreasing with increasing density, 1< D<3. The average distance between particles is computed in Monte Carlo simulations and analytically in the mean field approach. A dramatic drop at the phase transition is exhibited, clearly illustrating the properties of the collapsePrimary Subject

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S0550321302000263; Copyright (c) 2002 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: Pakistan

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Vega, H.J. de; Sanchez, N., E-mail: devega@lpthe.jussieu.fr

AbstractAbstract

[en] We provide a complete picture to the self-gravitating non-relativistic gas at thermal equilibrium using Monte Carlo simulations, analytic mean field methods (MF) and low density expansions. The system is shown to possess an infinite volume limit in the grand canonical (GCE), canonical (CE) and microcanonical (MCE) ensembles when (N,V)→∞, keeping N/V

^{1/3}fixed. We compute the equation of state (we do not assume it as is customary), as well as the energy, free energy, entropy, chemical potential, specific heats, compressibilities and speed of sound; we analyze their properties, signs and singularities. All physical quantities turn out to depend on a single variable η≡((Gm^{2}N)/(V^{1/3}T)) that is kept fixed in the N→∞ and V→∞ limit. The system is in a gaseous phase for η<η_{T}and collapses into a dense object for η>η_{T}in the CE with the pressure becoming large and negative. At η≅η_{T}the isothermal compressibility diverges. This gravitational phase transition is associated to the Jeans' instability. Our Monte Carlo simulations yield η_{T}≅1.515. PV/[NT]=f(η) and all physical magnitudes exhibit a square root branch point at η=η_{C}>η_{T}. The values of η_{T}and η_{C}change by a few percent with the geometry for large N: for spherical symmetry and N=∞ (MF), we find η_{C}=1.561764... while the Monte Carlo simulations for cubic geometry yields η_{C}≅1.540. In mean field and spherical symmetry c_{V}diverges as (η_{C}-η)^{-1/2}for η↑η_{C}while c_{P}and κ_{T}diverge as (η_{0}-η)^{-1}for η↑η_{0}=1.51024.... The function f(η) has a second Riemann sheet which is only physically realized in the MCE. In the MCE, the collapse phase transition takes place in this second sheet near η_{MC}=1.26 and the pressure and temperature are larger in the collapsed phase than in the gaseous phase. Both collapse phase transitions (in the CE and in the MCE) are of zeroth order since the Gibbs free energy has a jump at the transitions. The MF equation of state in a sphere, f(η), obeys a first order non-linear differential equation of first kind Abel's type. The MF gives an extremely accurate picture in agreement with the MC simulations both in the CE and MCE. Since we perform the MC simulations on a cubic geometry they describe an isothermal cube while the MF calculations describe an isothermal sphere. The local properties of the gas, scaling behaviour of the particle distribution and its fractal (Haussdorf ) dimension are investigated in the companion paper quoted as paper II in the text: H.J. de Vega, N. Sanchez, astro-ph/0101567, next paper in this issuePrimary Subject

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S0550321302000251; Copyright (c) 2002 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: Pakistan

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[en] New solutions of self-dual Yang-Mills (SDYM) equations are constructed in Minkowski space-time for the gauge group SL(2,C). After proposing a Lorentz covariant formulation of Yang's equations, a set of Ansaetze for exact non-linear multiplane wave solutions are proposed. The gauge fields are rational functions of e

^{x.k}i(k_{i}^{2}= 0,1 ≤ i ≤ N) for these Ansaetze. At least, three families of multisoliton type solutions are derived explicitly. Their asymptotic behaviour shows that non-linear waves scatter non-trivially in Minkowski SDYM. (orig.)Primary Subject

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Boyanovsky, D.; Cao, F.J.; Vega, H.J. de, E-mail: devega@lpthe.jussieu.fr

AbstractAbstract

[en] We investigate inflation driven by the evolution of highly excited quantum states within the framework of out of equilibrium field dynamics. These states are characterized by a non-perturbatively large number of quanta in a band of momenta but with vanishing expectation value of the scalar field. They represent the situation in which initially a non-perturbatively large energy density is localized in a band of high energy quantum modes and are coined tsunami-waves. The self-consistent evolution of this quantum state and the scale factor is studied analytically and numerically. It is shown that the time evolution of these quantum states lead to two consecutive stages of inflation under conditions that are the quantum analogue of slow-roll. The evolution of the scale factor during the first stage has new features that are characteristic of the quantum state. During this initial stage the quantum fluctuations in the highly excited band build up an effective homogeneous condensate with a non-perturbatively large amplitude as a consequence of the large number of quanta. The second stage of inflation is similar to the usual classical chaotic scenario but driven by this effective condensate. The excited quantum modes are already superhorizon in the first stage and do not affect the power spectrum of scalar perturbations. Thus, this tsunami quantum state provides a field theoretical justification for chaotic scenarios driven by a classical homogeneous scalar field of large amplitude

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S0550321302002389; Copyright (c) 2002 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: Syrian Arab Republic

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[en] We quantize a closed bosonic string in a light-cone gauge in Rindler (uniformly accelerated) space-time and apply it to the Schwarzschild-Kruskal manifold. Inertial and accelerated particle states of the string associated to positive frequency modes with respect to the inertial and Rindler times respectively, are defined. There is a stretching effect of the string due to the presence of an event horizon. We explicitly solve the dynamical constraints leaving as physical degrees of freedom only those transverse to the acceleration. Different mass formulae are introduced depending on whether the centre of mass of the string has uniform speed or uniform acceleration. The expectation value of the Rindler (Schwarzschild) number-mode operator in the string ground state (tachyon) results equal to a thermal spectrum at the Hawking-Unruh temperature T

_{s}= α/2π (∝ M_{Pl}(M_{Pl}/M)^{1/(D-3)}, where M is the black hole mass). We find T_{0}= M'/2π where M' is the accelerated ground state string mass and T_{0}the temperature T_{s}in dimensionless frequency units. Correlation functions of string coordinates and vertex operators and their Fourier transforms in accelerated time (string response functions) are computed and their thermal properties analyzed. (orig.)Primary Subject

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ACCELERATION, ANNIHILATION OPERATORS, BLACK HOLES, BOSONS, CORRELATION FUNCTIONS, CORRELATIONS, CREATION OPERATORS, EIGENVALUES, EXPECTATION VALUE, FOURIER TRANSFORMATION, GEODESICS, GROUND STATES, LAGRANGIAN FIELD THEORY, LIGHT CONE, MANY-DIMENSIONAL CALCULATIONS, MASS FORMULAE, RESPONSE FUNCTIONS, REST MASS, RIEMANN SPACE, SCHWARZSCHILD METRIC, SECOND QUANTIZATION, SMOOTH MANIFOLDS, SPECTRA, STRING MODELS, TACHYONS, VERTEX FUNCTIONS

ELEMENTARY PARTICLES, ENERGY LEVELS, EXTENDED PARTICLE MODEL, FIELD THEORIES, FUNCTIONS, INTEGRAL TRANSFORMATIONS, MASS, MATHEMATICAL MANIFOLDS, MATHEMATICAL MODELS, MATHEMATICAL OPERATORS, MATHEMATICAL SPACE, METRICS, PARTICLE MODELS, POSTULATED PARTICLES, QUANTIZATION, QUANTUM FIELD THEORY, QUANTUM OPERATORS, SPACE, SPACE-TIME, TRANSFORMATIONS

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[en] We develop a general scheme for solving the equations of motion and constraints of strings in curved spacetimes, both classically and quantum mechanically. We treat the spacetime geometry exactly and the string excitations small as compared with the energy scales of the metric. [The perturbation (dimensionless) parameter is g = √(πα')/R

_{c}where √α' = l_{Pl}is the Planck length and R_{c}the typical curvature radius of the geometry.] This formalism is particularly well suited to properly consider strings in the context of quantum black holes and cosmology. As an illustration we apply it to de Sitter spacetime and find the mass spectrum and vertex operator. The lower mass states are the same as in flat space up to corrections of order g^{2}whereas heavy states deviate significantly from the linear Regge trajectories. We find a maximum (very large) value of order 1/g^{2}for the quantum number N and spin J of particles. The critical dimension for bosonic strings is found to be 25 in de Sitter spacetime. (orig.)Primary Subject

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[en] Two-dimensional fermionic field theories are defined on a diagonal lattice obtained by discretizing Minkowski space-time in light-cone coordinates. This approach leads to local second-quantized equations of motion on the lattice. The contimuun limit is carefully performed, yielding the massive Thirring model whenever fermions without internal structure are considered. The exact eigenstates and eigenvalues constructed in this lattice formalism confirm the known Bethe ansatz equations of the massive Thirring model. The light-cone lattice approach brings a class of integrable fermion models within the general algebraic scheme of the quantum inverse scattering method. (orig.)

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ALGEBRA, ASYMPTOTIC SOLUTIONS, CHIRALITY, DISPERSION RELATIONS, EIGENSTATES, EIGENVALUES, FERMIONS, FIELD EQUATIONS, HAMILTONIANS, INVERSE SCATTERING PROBLEM, LAGRANGE EQUATIONS, LAGRANGIAN FIELD THEORY, LATTICE FIELD THEORY, LIGHT CONE, LINEAR MOMENTUM OPERATORS, MINKOWSKI SPACE, REST MASS, S MATRIX, SCATTERING AMPLITUDES, SECOND QUANTIZATION, SPINOR FIELDS, THIRRING MODEL, TRANSFER MATRIX METHOD, TWO-DIMENSIONAL CALCULATIONS

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[en] The light-cone lattice approach to two-dimensional quantum field theories is generalized to a large class of vertex models with any number of possible states per link and any simple Lie group of symmetry. Starting from a given lattice model, different scaling limits are defined leading to conformal field theories or to massive integrable quantum field theories, for which the lattice hamiltonian, momentum and currents are constructed. For a large set of models, the complete mass spectrum is also exhibited. Our approach applies equally well to chiral fermionic theories (like the chiral Gross-Neveu) and to bosonic models like the principal chiral model. (orig.)

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