Quantization of solitons and the restricted sine-Gordon model

We show how to compute form factors, matrix elements of local fields, in the restricted sine-Gordon model, at the reflectionless points, by quantizing solitons. We introduce (quantum) separated variables in which the Hamiltonians are expressed in terms of (quantum) τ-functions. We explicitly describe the soliton wave functions, and we explain how the restriction is related to an unusual hermitian structure. We also present a semi-classical analysis which enlightens the fact that the restricted sine-Gordon model corresponds to an analytical continuation of the sine-Gordon model, intermediate between sine-Gordon and KdV. Laboratoire associé au CNRS. Laboratoire de la Direction des Sciences de la Matière du Commissariat à l'Energie Atomique.     

Hidden Yangians in 2D massive current algebras

We define non-local conserved currents in massive current algebras in two dimensions. Our approach is algebraic and non-perturbative. The non-local currents give a quantum field realization of the Yangians. We show how the noncocommutativity of the Yangians is related to the non-locality of the currents. We discuss the implications of the existence of non-local conserved charges on theS-matrices.Laboratoire de la Direction des sciences de la matière du Commissariat à l'énergie atomique     

Fusion and singular vectors inA 1 (1) highest weight cyclic modules

We show how the interplay between the fusion formalism of conformal field theory and the Knizhnik-Zamolodchikov equation leads to explicit formulae for the singular vectors in the highest weight representations ofA ₁ ⁽¹⁾ .Laboratoire de la Direction des Sciences de la Matière du Commissariat à l'Energie Atomique     

ClassicalW-algebras

We reconsider the relation between classicalW-algebras and deformations of differential operators, emphasizing the consistency with diffeomorphisms. Generators of theW-algebra that arek-differentials are constructed by a systematic procedure. The method extends, following Drinfeld and Sokolov, toW-algebras based on arbitrary simple Lie algebras.Laboratoire de la Direction des Sciences de la Matière du Commissariat à l'Energie Atomique     

Cosmological constant and lensing

The effect of the cosmological constant on the curvature of light due to an isolated spherical mass is recalculated without using the lens equation and compared to a lensing cluster. Unité Mixte de Recherche (UMR 6207) du CNRS et des Universités Aix–Marseille 1 et 2 et Sud Toulon–Var, Laboratoire affilié à la FRUMAM (FR 2291).     

Soft photon production rate in resummed perturbation theory of high temperature QCD

We calculate the production rate of soft real photons from a hot quark-gluon plasma using Braaten-Pisarski's perturbative resummation method. To leading order in the QCD coupling constantg we find a logarithmically divergent result for photon energies of ordergT, whereT is the plasma temperature. This divergent behaviour is due to unscreened mass singularities in the effective hard thermal loop vertices in the case of a massless external photon.Laboratoire associé du Centre National de la Recherche Scientifique     

Instantaneous frequencies of a chaotic system

The structure and geometry of high-dimensional, complex dynamical systems is usually hidden under a profusion of numerical data. We show that time-frequency analysis allows one to analyze these data regardless of the number of degrees of freedom. Our method takes snapshots of the system in terms of its instantaneous frequencies defined as ridges of the time-frequency landscape. Using the wavelet transform of a single trajectory, it can characterize key dynamical properties like the extent of chaos, resonance transitions and trappings. Unité Mixte de Recherche (UMR 6207) du CNRS, et des universités Aix-Marseille I, Aix-Marseille II et du Sud Toulon-Var. Laboratoire affilié à la FRUMAM (FR 2291).     

Spectral stability under tunneling

We study the spectral properties of multiple well Schrödinger operators on ⁿ . We give in particular upper bounds on energy shifts due to tunnel effect and localization properties of wave packets. Our methods are based on Agmon type estimates for resolvents in classically forbidden regions and geometric perturbation theory. Our results are valid also for an infinite number of wells, arbitrary spectral type and in non-semi-classical regimes.Laboratoire Propre, Centre National de la Recherche ScientifiquePhymat, Université de Toulon et du Var     

Causality in local quantum field theory: Some general results

General asymptotic causality properties of chronologicalN-point functions and, in massive theories, ofN-particle collision amplitudes, are derived from locality and the spectral condition. Results include specified rates of exponential fall-off, with simple and direct physical content, for large non-causal separations of points or particles in Minkowski space-time depending on values of the energy-momenta and on the mass spectrum. Relevant mathematical results on rates of exponential fall-off of generalized Fourier transforms outside their microsupports are given.Laboratoire de la Direction des Sciences de la Matière du Commissariat à l'Energie Atomique     

Matrix integration and combinatorics of modular groups

Integration over Gaussian matrix ensembles was used to obtain the virtual Euler characteristics of mapping class groups. We present some simplifications in the combinatorial part of the calculation.Laboratoire de l'Institut de Recherche Fondamentale du Commissariat à l'Energie Atomique     

Spin effects in the electron structure functions

The electron structure functions are studied in polarized e ⁺ e ^- scattering. The formulae for longitudinally and transversely polarized electrons are presented. The smallness of the electron mass leads to negligible cross-sections and asymmetries in some cases. Positivity constraints on the structure functions and parton densities are constructed and discussed. The cross-section asymmetries at very high energies, where the inclusion of all elecroweak bosons is necessary, are calculated. Numerical examples, using the asymptotic solutions for the parton densities inside the electron, are presented.Received: 23 June 2004, Revised: 26 October 2004, Published online: 17 December 2004PACS: 12.15.Ji, 12.38.QkJ. Szwed: Work supported by the European Commission contract ICA1-CT-2002-70013/INCO Strategic action on training and excellence, 5FP.Unité Mixte de Recherche du CNRS et des Universités de Provence, de la Méditerranée et du Sud Toulon-Var - Laboratoire affilié a la FRUNAM - FR 2291, CNRS-Luminy, Case 907, 13288 Marseille Cedex 9, France.     

Harmonic analysis on the Poincaré group

The generalized matrix elements on the Poincaré group are used to write the Fourier transform explicitly. This realizes a mapping between positive type functions on the group and generalized density matrices.Laboratoire associé au Centre National de la Recherche Scientifique.     

On the first-order operators in bimodules

We analyse the structure of the first-order operators in bimodules introduced by A. Connes. We apply this analysis to the theory of connections on bimodules, thereby generalizing several proposals.Laboratoire associé au Centre National de la Recherche Scientifique — URA D0063.     

Monotonicity of ionization energies for three electron lithium-type systems

Although it is quite obvious that an increasing amount of energy is required to remove more and more electrons from an atom, the proof of this observation seems to be a remarkably difficult problem in mathematical physics. Here, by using well-known energy bounds, we show the monotonicity of ionization energies for the simplest nontrivial system, i.e., a nucleus (with infinite mass) and three electrons, which physically corresponds to ionization in the lithium isoelectronic series via the para-channel.PHYMAT, Dept. de math. Univ. de Toulon et du Var F-83130 La Garde, France.On leave from Stranski Institut, TEL 33 Tech. Univ. Berlin D-1000 Berlin 10, F.R.G.Laboratoire propre du Centre Nationale de la Recherche Scientifique.     

Power series for level spacing functions of random matrix ensembles

A remarkable set of identities among (odd and even) spheroidal functions and their eigenvalues is indicated. This is then used to derive explicitly the general term in the power series expansion ofE (r, s), the probability that a randomly chosen interval of lengths contains exactlyr levels. The parameter takes the values 1, 2 or 4 according as the ensemble considered is orthogonal, unitary or symplectic.Laboratoire de la Direction des Sciences de la Matière du Commissariat à l'Energie Atomique     

Kazama-Suzuki models as shifted bosonic lattices

Some Kazama-Suzuki models admit a realization in terms of free bosons defined on a lattice. A criterion for such a realization and its construction are presented. Some examples are worked out.URA 14-36 du CNRS, associée à l'Ecole Normale Supérieure de Lyon et au Laboratoire d'Annecy-le-Vieux de Physique des Particules.     

Spectral Action on <Emphasis Type="Italic">SU</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(2)

The spectral action on the equivariant real spectral triple over is computed explicitly. Properties of the differential calculus arising from the Dirac operator are studied and the results are compared to the commutative case of the sphere . UMR 6207, – Unité Mixte de Recherche du CNRS et des Universités Aix-Marseille I, Aix-Marseille II et de l’Université du Sud Toulon-Var, Laboratoire affilié à la FRUMAM – FR 2291. Partially supported by Polish Government grants 189/6.PRUE/2007/7; 115/E-343/SPB/6.PR UE/DIE and N 201 1770 33.     

On heavy Higgs boson production

We develop the technique for calculating interference effects in the effective-W boson method. We find that these effects produce a very large azimuthal asymmetry for single Higgs boson production, which could be used as identification of the process. We also find that the cross section of Higgs boson pair production strongly depends on Higgs self-interaction, and for non-standard models of Higgs bosons could be 5 or 10 times larger than in the case of the standard one.Laboratoire associé au Centre National de la Recherche Scientifique     

Anisotropic hubble expansion of large scale structures

With the aim of understanding the cosmic velocity fields at large scale, we investigate the dynamics of a pressureless distribution of gravitational sources moving under an anisotropic generalization of Hubble expansion and according to Euler-Poisson equations system. As a result, it turns out that such a behavior requires the distribution to be homogenous, similarly to Hubble law. Among several solutions, we show a planar kinematics which admits a constant (eternal) and rotational distortion, where the velocity field is not potential. Within this class, the one with no rotational distortion identifies to a bulk flow. To apply this model within cosmic structures as the Local Super Cluster, the solutions are interpreted as approximations providing us with an hint on the behavior of the cosmic flow just after decoupling era up to present date. Such a result suggests that the observed bulk flow may not be due exclusively to tidal forces but has a primordial origin. UPRES EA 2596. Unité Mixte de Recherche (UMR 6207) du CNRS, et des universités Aix-Marseille I, Aix-Marseille II et du Sud Toulon-Var. Laboratoire affiliéà la FRUMAM (FR 2291).     

Excitation d'ondes acoustiques par une flamme

Acoustic waves have been excited in a flame seeded with potassium. We show that the amplitude of the excited wave is proportional to the frequency of a harmonic perturbation imposed on the plasma. This suggests a means of ultrasonic excitation, the limitations of which are analysed.

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Laboratoire Associé au Centre National de la Recherche Scientifique (C.N.R.S.).