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

Bose enhancement, the Liouville effective action and the high multiplicity tail in p-A collisions

In the framework of dense-dilute CGC approach we study fluctuations in the multiplicity of produced particles in p-A collisions. We show that the leading effect that drives the fluctuations is the Bose enhancement of gluons in the proton wave function. We explicitly calculate the moment generating function that resums the effects of Bose enhancement. We show that it can be understood in terms of the Liouville effective action for the composite field which is identified with the fluctuating density, or saturation momentum of the proton. The resulting probability distribution turns out to be very close to the gamma-distribution. We also calculate the first correction to this distribution which is due to pairwise Hanbury Brown-Twiss correlations of produced gluons.Comment: 15 pages, 3 figures; version accepted for publicatio

Consistent axial--like gauge fixing on hypertori

We analyze the Gribov problem for \SU(N) and \U(N) Yang-Mills fields on $d$-dimensional tori, $d=2,3,\ldots$. We give an improved version of the axial gauge condition and find an infinite, discrete group \cG'=\Z^{dr}\rtimes({\Z_2}^{N-1}\rtimes\Z_2), where $r=N-1$ for \GG=\SU(N) and $r=N$ for \GG=\U(N), containing all gauge transformations compatible with that condition. This residual gauge group \cG' provides (generically) all Gribov copies and allows to explicitly determine the space of gauge orbits which is an orbifold. Our results apply to Yang-Mills gauge theories either in the Lagrangian approach on $d$-dimensional space-time $T^d$, or in the Hamiltonian approach on $(d+1)$-dimensional space-time $T^d\times \R$. Using the latter, we argue that our results imply a non-trivial structure of all physical states in any Yang-Mills theory, especially if also matter fields are present.Comment: 12 pages, UBCTP 93-13, LA-UR-93-299