Variational techniques in non-perturbative QCD

We review attempts to apply the variational principle to understand the vacuum of non-abelian gauge theories. In particular, we focus on the method explored by Ian Kogan and collaborators, which imposes exact gauge invariance on the trial Gaussian wave functional prior to the minimization of energy. We describe the application of the method to a toy model -- confining compact QED in 2+1 dimensions -- where it works wonderfully and reproduces all known non-trivial results. We then follow its applications to pure Yang-Mills theory in 3+1 dimensions at zero and finite temperature. Among the results of the variational calculation are dynamical mass generation and the analytic description of the deconfinement phase transition.Comment: 71 pages, 1 figure. To be published in the memorial volume "From Fields to Strings: Cirvumnavigating Theoretical Physics", World Scientific, 2004. Dedicated to the memory of Ian Koga

Asymmetric dynamics and critical behavior in the Bak-Sneppen model

We investigate, using mean-field theory and simulation, the effect of asymmetry on the critical behavior and probability density of Bak-Sneppen models. Two kinds of anisotropy are investigated: (i) different numbers of sites to the left and right of the central (minimum) site are updated and (ii) sites to the left and right of the central site are renewed in different ways. Of particular interest is the crossover from symmetric to asymmetric scaling for weakly asymmetric dynamics, and the collapse of data with different numbers of updated sites but the same degree of asymmetry. All non-symmetric rules studied fall, independent of the degree of asymmetry, in the same universality class. Conversely, symmetric variants reproduce the exponents of the original model. Our results confirm the existence of two symmetry-based universality classes for extremal dynamics.Comment: 14 pages, 8 figures, 1 tabl

Forward-Backward rapidity correlations at all rapidities

We discuss forward-bacward rapidity correlations in the general situation of asymmetrical collisions, asymmetric rapidity windows, higher rapidities and higher energy. We give predictions for RHIC and LHC.Comment: 6 pages, 3 figure

Variational analysis of the deconfinement phase transition

We study the deconfining phase transition in 3+1 dimensional pure SU(N) Yang-Mills theory using a gauge invariant variational calculation. We generalize the variational ansatz of Phys. Rev. D52, 3719 (1995) to mixed states (density matrices) and minimize the free energy. For N > 3 we find a first order phase transition with the transition temperature of T_C = 450 Mev. Below the critical temperature the Polyakov loop has vanishing expectation value, while above T_C, its average value is nonzero. According to the standard lore this corresponds to the deconfining transition. Within the accuracy of our approximation the entropy of the system in the low temperature phase vanishes. The latent heat is not small but, rather, is of the order of the nonperturbative vacuum energy.Comment: 15 pages, correction of minor typos only, submitted to JHE

On the cosmological effects of the Weyssenhoff spinning fluid in the Einstein-Cartan framework

The effects of non-Riemannian structures in Cosmology have been studied long ago and are still a relevant subject of investigation. In the seventies, it was discovered that singularity avoidance and early accelerated expansion can be induced by torsion in the Einstein-Cartan theory. In this framework, torsion is not dynamical and is completely expressed by means of the spin sources. Thus, in order to study the effects of torsion in the Einstein-Cartan theory, one has to introduce matter with spin. In principle, this can be done in several ways. In this work we consider the cosmological evolution of the universe in the presence of a constant isotropic and homogeneous axial current and the Weyssenhoff spinning fluid. We analyse possible solutions of this model, with and without the spinning fluid.Comment: Work presented at the 7th Alexander Friedmann International Seminar on Gravitation and Cosmology, Joao Pessoa, Brazil, 29 Jun - 5 Jul 2008. No figures, 5 pages. New version with dynamical equation corrected, new reference and a brief comparison with its experimental bound