Jacek Wosiek

Distribution of the color fields around static quarks: Flux tube profiles.

We report detailed calculations of the profiles of energy and action densities in the quark-antiquark string in SU(2) lattice gauge theory. We conclude that at a {ital q}-{ital q}{vert_bar} separation {ital R}{approx_equal}1.0 fm we are beginning to see the asymptotic flux tube. By employing the Michael sum rules we further conclude that the peak energy density approaches a constant in {ital R}. {copyright} {ital 1995 The American Physical Society.}

Intermittency and other correlation phenomena in high energy collisions

Abstract We discuss the phenomenology of multiplicity fluctuations in small phase space cells (“intermittency”) in connection with correlation functions and negative binomial fits. Whereas soft collisions show smooth, roughly energy independent short-range rapidity correlations, strong short-range correlations are expected to build up in e + e − annihilation with increasing energy and should become visible at LEP energies. We address the question to what extent present data can be explained by jet models and propose further tests. An anomalous collective effect is observed in nucleus-nucleus collisions which deserves further verification.

Positive representations of a class of complex measures

We study the problem of constructing positive representations of complex measures. In this paper we consider complex densities on a direct product of

Energy and action of the colour fields around static quarks

U(1)

High precision study of the space distribution of the colour flux in the SU(2) lattice gauge theory

groups and look for representations by probability distributions on the complexification of those groups. After identifying general necessary and sufficient conditions we propose several concrete realizations. Finally we study some of those realizations in examples representing problems in abelian lattice gauge theories.

Beyond Complex Langevin Equations: positive representation of a class of complex measures

Abstract Results on the profiles of the confining tube in the energy and action densities are discussed. Lattice sum rules are tested in detail.

Beyond complex Langevin equations

Abstract The work of the Cracow-LSU collaboration on the space structure of the colour fields around the static charges is reported. We find that the large cancellations between the electric and magnetic energy densities lead to a narrow tube.

Lipatov pomeron and the Heisenberg chain

A positive representation for a set of complex densities is constructed. In particular, complex measures on a direct product of U(1) groups are studied. After identifying general conditions which such representations should satisfy, several explicit realizations are proposed. Their utility is illustrated in few concrete examples representing problems in abelian lattice gauge theories.

Distribution of the color fields around static quarks: Lattice sum rules

A simple integral relation between a complex weight and the corresponding positive distribution is derived by introducing a second complex variable. Together with the positivity and normalizability conditions, this sum rule allows to construct explicitly equivalent pairs of distributions in simple cases. In particular the well known solution for a complex gaussian distribution is generalized to an arbitrary complex slope. This opens a possibility of positive representation of Feynman path integrals directly in the Minkowski time. Such construction is then explicitly carried through in the second part of this presentation. The continuum limit of the new representation exists only if some of the additional couplings tend to infinity and are tuned in a specific way. The approach is then successfully applied to three quantum mechanical examples including a particle in a constant magnetic field -- a simplest prototype of a Wilson line. Further generalizations are shortly discussed and an amusing interpretation of new variables is briefly mentioned.

The perturbative odderon intercept

It is pointed out that the recently discovered analogy between the QCD description of the Pomeron exchange and the Heisenberg chain may allow applying lattice techniques to the high energy phenomena.