Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

We consider the Hamiltonian reduction of the two-loop Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra script Ĝ. The resulting reduced models, called Generalized Non-Abelian Conformal Affine Toda (G-CAT), are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-Abelian generalizations of the conformal affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the τ-functions, which are defined for any integrable highest weight representation of script Ĝ, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed. We also introduce what we call the two-loop Virasoro algebra, describing extended symmetries of the two-loop WZNW models.

On closed Einstein-de Sitter universes

We briefly summarize the idea of cosmological models with compact, flat spatial sections. It has been suggested that, because of the COBE satellite's maps of the microwave background, such models cannot be small in the sense of Ellis, and hence are no longer interesting. Here we use the method of cosmic crystallography by Lehoucq et al. to show that these models are physically meaningful even if the size of the spatial sections is of the same order of magnitude as the radius of the observational horizon. © 1998 Elsevier Science B.V.

First-order perturbed Korteweg-de Vries solitons

We consider the Korteweg-de Vries equation with a perturbation arising naturally in many physical situations. Although being asymptotically integrable, we show that the corresponding perturbed solitons do not have the usual scattering properties. Specifically, we show that there is a solution, correct up to O(ε), where ε is the perturbative parameter, consisting, at t→ -∞ of two superposed deformed solitons characterized by wave numbers k1 and k2 that give rise, for t→ +∞, to the same but phase-shifted superposed solitons plus a coupling term depending on k1, and k2. We also find the condition on the original equation for which this coupling vanishes.

Relativistic quantum thermodynamics of ideal gases in two dimensions

In this work we study the behavior of relativistic ideal Bose and Fermi gases in two space dimensions. Making use of polylogarithm functions we derive a closed and unified expression for their densities. It is shown that both type of gases are essentially inequivalent, and only in the non-relativistic limit the spinless and equal mass Bose and Fermi gases are equivalent as known in the literature.

Confinement, solitons and the equivalence between the sine-Gordon and massive Thirring models

We consider a two-dimensional integrable and conformally invariant field theory possessing two Dirac spinors and three scalar fields. The interaction couples bilinear terms in the spinors to exponentials of the scalars. Its integrability properties are based on the sl(2) affine Kac-Moody algebra, and it is a simple example of the so-called conformal affine Toda theories coupled to matter fields. We show, using bosonization techniques, that the classical equivalence between a U(1) Noether current and the topological current holds true at the quantum level, and then leads to a bag model like mechanism for the confinement of the spinor fields inside the solitons. By bosonizing the spinors we show that the theory decouples into a sine-Gordon model and free scalars. We construct the two-soliton solutions and show that their interactions lead to the same time delays as those for the sine-Gordon solitons. The model provides a good laboratory to test duality ideas in the context of the equivalence between the sine-Gordon and Thirring theories. © 2000 Elsevier Science B.V. All rights reserved.

Gravitational Energy-Momentum Density in Teleparallel Gravity

In the context of a gauge theory for the translation group, a conserved energy-momentum gauge current for the gravitational field is obtained. It is a true spacetime and gauge tensor, and transforms covariantly under global Lorentz transformations. By rewriting the gauge gravitational field equation in a purely spacetime form, it becomes the teleparallel equivalent of Einstein's equation, and the gauge current reduces to the Møller's canonical energy-momentum density of the gravitational field.

Quantum vacuum in hot nuclear matter: A non-perturbative treatment

We derive the equation of state for hot nuclear matter using the Walecka model in a non-perturbative formalism. We include here the vacuum polarization effects arising from the nucleon and scalar mesons through a realignment of the vacuum. A ground state structure with baryon-antibaryon condensates yields the results obtained through the relativistic Hartree approximation of summing baryonic tadpole diagrams. Generalization of such a state to include the quantum effects for the scalar meson fields through the σ -meson condensates amounts to summing over a class of multiloop diagrams. The techniques of the thermofield dynamics method are used for the finite-temperature and finite-density calculations. The in-medium nucleon and sigma meson masses are also calculated in a self-consistent manner. We examine the liquid-gas phase transition at low temperatures (≈ 20 MeV), as well as apply the formalism to high temperatures to examine a possible chiral symmetry restoration phase transition.

Confinement and soliton solutions in the SL(3) Toda model coupled to matter fields

We consider an integrable conformally invariant two-dimensional model associated to the affine Kac-Moody algebra sl3(ℂ). It possesses four scalar fields and six Dirac spinors. The theory does not possesses a local Lagrangian since the spinor equations of motion present interaction terms which are bilinear in the spinors. There exists a submodel presenting an equivalence between a U(1) vector current and a topological current, which leads to a confinement of the spinors inside the solitons. We calculate the one-soliton and two-soliton solutions using a procedure which is a hybrid of the dressing and Hirota methods. The soliton masses and time delays due to the soliton interactions are also calculated. We give a computer program to calculate the soliton solutions. © 2002 Published by Elsevier Science B.V.

Integrability and conformal symmetry in higher dimensions: A model with exact hopfion solutions

We use ideas on integrability in higher dimensions to define Lorentz invariant field theories with an infinite number of local conserved currents. The models considered have a two-dimensional target space. Requiring the existence of lagrangean and the stability of static solutions singles out a class of models which have an additional conformal symmetry. That is used to explain the existence of an ansatz leading to solutions with non-trivial Hopf charges. © SISSA/ISAS 2002.

Soliton propagation in a medium with Kerr nonlinearity and resonant impurities: A variational approach

The soliton propagation in a medium with Kerr nonlinearity and resonant impurities was studied by a variational approach. The existence of a solitary wave was shown within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations. The analytical solution which was obtained, was tested through numerical simulations confirming its solitary wave nature.

Classical versus quantum equivalence between sine-Gordon, Liouville and other solitons

In this work we present a mapping between the classical solutions of the sine-Gordon, Liouville, λφ4 and other kinks in 1+1 dimensions. This is done by using an invariant quantity which relates the models. It is easily shown that this procedure is equivalent to that used to get the so called deformed solitons, as proposed recently by Bazeia et al. [Phys. Rev. D. 66 (2002) 101701(R)]. The classical equivalence is explored in order to relate the solutions of the corresponding models and, as a consequence, try to get new information about them. We discuss also the difficulties and consequences which appear when one tries to extend the deformation in order to take into account the quantum version of the models.

Measurement of the tt̄ production cross section in pp̄ collisions at √s = 1.96 TeV in dilepton final states

We present a measurement of the top quark pair (tt̄) production cross section in pp̄ collisions at √s=1.96 TeV using events with two charged leptons in the final state. This analysis utilizes an integrated luminosity of 224-243 pb-1 collected with the DØ detector at the Fermilab Tevatron Collider. We observe 13 events in the e+e -, eμ and μ+μ- channels with an expected background of 3.2±0.7 events. For a top quark mass of 175 GeV, we measure a tt̄ production cross section of σtt̄=8. 6-2.7 +3.2(stat)±1.1(syst)±0.6(lumi) pb, consistent with the standard model prediction. © 2005 Elsevier B.V. All rights reserved.

Search for squarks and gluinos in events with jets and missing transverse energy in p(p)over-bar collisions at root s-=1.96 TeV

The results of a search for squarks and gluinos using data from p over(p, ̄) collisions recorded at a center-of-mass energy of 1.96 TeV by the DØ detector at the Fermilab Tevatron Collider are reported. The topologies analyzed consist of acoplanar-jet and multijet events with large missing transverse energy. No evidence for the production of squarks or gluinos was found in a data sample of 310 pb-1. Lower limits of 325 and 241 GeV were derived at the 95% C.L. on the squark and gluino masses, respectively, within the framework of minimal supergravity with tan β = 3, A0 = 0, and μ < 0. © 2006 Elsevier B.V. All rights reserved.

Search for associated Higgs boson production WH→WWW *→l±νl′±ν′+X in pp̄ collisions at s=1.96TeV

We present a search for associated Higgs boson production in the process pp̄→WH→WWW*→l±νl′±ν′ +X in final states containing two like-sign isolated electrons or muons (e±e±, e±μ±, or μ±μ±). The search is based on D0 run II data samples corresponding to integrated luminosities of 360-380pb-1. No excess is observed over the predicted standard model background. We set 95% C.L. upper limits on σ(pp̄→WH) ×Br(H→WW*) between 3.2 and 2.8 pb for Higgs boson masses from 115 to 175 GeV. © 2006 The American Physical Society.

Z gamma production and limits on anomalous ZZ gamma and Z gamma gamma couplings in pp collisions at root s=1.96 TeV

We present a study of eeγ and μμγ events using 1109 (1009) pb-1 of data in the electron (muon) channel, respectively. These data were collected with the DØ detector at the Fermilab Tevatron p over(p, ̄) collider at sqrt(s) = 1.96   TeV. Having observed 453 (515) candidates in the eeγ (μμγ) final state, we measure the Zγ production cross section for a photon with transverse energy ET > 7   GeV, separation between the photon and leptons Δ Rℓ γ > 0.7, and invariant mass of the di-lepton pair Mℓ ℓ > 30   GeV / c2, to be 4.96 ± 0.30 (stat . + syst .) ± 0.30 (lumi .)   pb, in agreement with the Standard Model prediction of 4.74 ± 0.22   pb. This is the most precise Zγ cross section measurement at a hadron collider. We set limits on anomalous trilinear Zγγ and ZZγ gauge boson couplings of - 0.085 < h30 γ < 0.084, - 0.0053 < h40 γ < 0.0054 and - 0.083 < h30 Z < 0.082, - 0.0053 < h40 Z < 0.0054 at the 95% C.L. for the form-factor scale Λ = 1.2   TeV.