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

New Perturbed Proximal Point Algorithms for Set-valued Quasi Variational Inclusions

In this paper, by using some new and innovative techniques, some perturbed iterative algorithms for solving generalized set-valued variational inclusions are suggested and analyzed. Since the generalized set-valued variational inclusions include many variational inclusions , variational inequalities and set-valued operator equation studied by others in recent years, the results obtained in this paper continue to hold for them and represent a significant refinement and improvement of the previously known results in this area

Relaxation Processes in Clouds of Trapped Bosons above the Bose-Einstein Condensation Temperature

We present a unified account of damping of low-lying collective modes and of relaxation of temperature anisotropies in a trapped Bose gas in the collisionless regime. By means of variational techniques, we show that the relaxation times for the two situations are closely related to the simplest variational estimate of the viscous relaxation time. We derive rather precise theoretical expressions for the characteristic relaxation times, and compare our results with experiment.Comment: 4 pages, revte