F. Lenz

Hamiltonian formulation of two-dimensional gauge theories on the light cone

In Quantum Chromodynamics, the theory of strong interactions, gluons and quarks are the microscopic degrees of freedom. Hadrons constitute the effective degrees of freedom in terms of which hadronic and nuclear reactions as well as nuclear structure are traditionally described. The fundamental problem of low energy strong interaction theory is to understand, within the framework of QCD, the transition from microscopic to phenomenological degrees of freedom. Quark models have been important in clarifying this relation between microscopic and effective degrees of freedom as far as the structure of single hadrons is concerned. As the historical development already indicates, compositeness together with a simple picture about the underlying confining dynamics is sufficient for a qualitative understanding of hadronic properties in terms of “constituent” quarks.

Confinement from merons

It is shown that an effective theory with meron degrees of freedom produces confinement in SU(2) Yang-Mills theory. When the scale is set by the string tension, the action density and topological susceptibility are similar to those arising in lattice QCD. The potential for this effective theory to produce center symmetry in SU(2) is discussed.

Quantum mechanics of the vacuum state in two-dimensional QCD with adjoint fermions

A study of two-dimensional QCD on a spatial circle with Majorana fermions in the adjoint representation of the gauge groups SU(2) and SU(3) is performed. The main emphasis is put on the symmetry properties related to the homotopically nontrivial gauge transformations and the discrete axial symmetry of this model. Within a gauge-fixed canonical framework, the delicate interplay of topology on the one hand and Jacobians and boundary conditions arising in the course of resolving Gauss`s law on the other hand is exhibited. As a result, a consistent description of the residual {ital Z}{sub {ital N}} gauge symmetry [for SU({ital N})] and the ``axial anomaly`` emerges. For illustrative purposes, the vacuum of the model is determined analytically in the limit of a small circle. There, the Born-Oppenheimer approximation is justified and reduces the vacuum problem to simple quantum mechanics. The issue of fermion condensates is addressed and residual discrepancies with other approaches are pointed out.

Confinement from Instantons or Merons

In contrast to ensembles of singular gauge instantons, which are well known to fail to produce confinement, it is shown that effective theories based on ensembles of merons or regular gauge instantons do produce confinement. Furthermore, when the scale is set by the string tension, the action density, topological susceptibility, and glueball masses are similar to those arising in lattice QCD.

Diffusion of Wilson loops

A phenomenological analysis of the distribution of Wilson loops in SU(2) Yang-Mills theory is presented in which Wilson loop distributions are described as the result of a diffusion process on the group manifold. It is shown that, in the absence of forces, diffusion implies Casimir scaling and, conversely, exact Casimir scaling implies free diffusion. Screening processes occur if diffusion takes place in a potential. The crucial distinction between screening of fundamental and adjoint loops is formulated as a symmetry property related to the center symmetry of the underlying gauge theory. The results are expressed in terms of an effective Wilson loop action and compared with various limits of SU(2) Yang-Mills theory.

Hadrons and hadronic matter

Quarks and Gluons in Hadrons and Nuclei.- Hadron Spectroscopy: an Overview with Strings Attached.- to Nambu Jona-Lasinio Models Applied to Low Energy Hadronic Matter.- The QCD Vacuum and Chiral Symmetry.- Hamiltonian Formulation of Two-Dirnensional Gauge theories on the Light-Cone.- Quark-Gluon Plasma and Space-Time Picture of Ultra-Relativistic Nuclear Collisions.- The Role of Quarks in Astrophysics.- Strangeness in the Skyrme Model.- Probing the Quark Structure of Matter.- Many-Body Theory of Nuclei and Nuclear Matter.- Limits on the Cosmic Baryon Density.- QCD and Hadrons on a Lattice.

Polyakov Loop Dynamics in the Center Symmetric Phase

Abstract A study of the center symmetric phase of SU(2) Yang–Mills theory is presented. Realization of the center symmetry is shown to result from non-perturbative gauge fixing. Dictated by the center symmetry, this phase exhibits already at the perturbative level confinement-like properties. The analysis is performed by investigating the dynamics of the Polyakov loops. The ultralocality of these degrees of freedom implies significant changes in the vacuum structure of the theory. General properties of the confined phase and of the transition to the deconfined phase are discussed. Perturbation theory built upon the vacuum of ultralocal Polyakov loops is presented and used to calculate, via the Polyakov loop correlator, the static quark– antiquark potential.

Confining effective theories based on instantons and merons

An effective theory based on ensembles of either regular gauge instantons or merons is shown to produce confinement in SU(2) Yang-Mills theory. When the scale is set by the string tension, the action density, topological susceptibility and low-lying glueball spectrum are similar to those arising in lattice QCD. The physical mechanism producing confinement is explained, and a number of analytical insights into the effective theory are presented.

Phases and Residual Gauge Symmetries of Higgs Models

Abstract After elimination of the redundant variables, gauge theories may still exhibit symmetries associated with the gauge fields. The role of these residual gauge symmetries is discussed within the Abelian Higgs model and the Georgi–Glashow model. In the different phases of these models, these symmetries are realized differently. The characteristics of emergence and disappearance of the symmetries are studied in detail and the implications for the dynamics in Coulomb, Higgs, and confining phases are discussed.

The pseudoparticle approach for solving path integrals in gauge theories

We present a numerical technique for calculating path integrals in non-compact U(1) and SU(2) gauge theories. The gauge fields are represented by a superposition of pseudoparticles of various types with their amplitudes and color orientations as degrees of freedom. Applied to Maxwell theory this technique results in a potential which is in excellent agreement with the Coulomb potential. For SU(2) Yang-Mills theory the same technique yields clear evidence of confinement. Varying the coupling constant exhibits the same scaling behavior for the string tension, the topological susceptibility and the critical temperature while their dimensionless ratios are similar to those obtained in lattice calculations.