Spin dependent potentials from SU(2) gauge theory

We present results on spin dependent potentials from lattice simulations of SU(2) gauge theory. The Coulomb like short range part of the central potential is identified as a mixed vector-scalar exchange while the linear long range part is pure scalar.Comment: Talk held at LAT 94 conference, 3 pages, latex, uses epscrc2.st

A Gauge and Lorentz covariant Approximation for the Quark Propagator in an arbitrary Gluon Field

We decompose the quark propagator in the presence of an arbitrary gluon field with respect to a set of Dirac matrices. The four-dimensional integrals which arise in first order perturbation theory are rewritten as line-integrals along certain field lines, together with a weighted integration over the various field lines. It is then easy to transform the propagator into a form involving path ordered exponentials. The resulting expression is non-perturbative and has the correct behavior under Lorentz transformations, gauge transformations and charge conjugation. Furthermore it coincides with the exact propagator in first order of the coupling g. No expansion with respect to the inverse quark mass is involved, the expression can even be used for vanishing mass. For large mass the field lines concentrate near the straight line connection and simple results can be obtained immediately.Comment: 15 pages, 3 figures. Replaced with version to appear in Eur. Phys. J.

Analytic approach to confinement and monopoles in lattice SU(2)

We extend the approach of Banks, Myerson, and Kogut for the calculation of the Wilson loop in lattice U(1) to the non-abelian SU(2) group. The original degrees of freedom of the theory are integrated out, new degrees of freedom are introduced in several steps. The centre group $Z_2$ enters automatically through the appearance of a field strength tensor $f_{\mu \nu}$, which takes on the values 0 or 1 only. It obeys a linear field equation with the loop current as source. This equation implies that $f_{\mu \nu}$ is non vanishing on a two-dimensional surface bounded by the loop, and possibly on closed surfaces. The two-dimensional surfaces have a natural interpretation as strings moving in euclidean time. In four dimensions we recover the dual Abrikosov string of a type II superconductor, i.e. an electric string encircled by a magnetic current. In contrast to other types of monopoles found in the literature, the monopoles and the associated magnetic currents are present in every configuration. With some plausible, though not generally conclusive, arguments we are directly led to the area law for large loops.Comment: 18 pages, uses latexsym, to appear in The European Physical Journal

On the Glue Content in Heavy Quarkonia

Starting with two coupled Bethe-Salpeter equations for the quark-antiquark, and for the quark-glue-antiquark component of the quarkonium, we solve the bound state equations perturbatively. The resulting admixture of glue can be partially understood in a semiclassical way, one has, however, to take care of the different use of time ordered versus retarded Green functions. Subtle questions concerning the precise definition of the equal time wave function arise, because the wave function for the Coulomb gluon is discontinuous with respect to the relative time of the gluon. A striking feature is that a one loop non abelian graph contributes to the same order as tree graphs, because the couplings of transverse gluons in the tree graphs are suppressed in the non relativistic bound state, while the higher order loop graph can couple to quarks via non suppressed Coulomb gluons. We also calculate the amplitude for quark and antiquark at zero distance in the quark-glue-antiquark component of the P-state. This quantity is of importance for annihilation decays of P-states. It shows a remarkable compensation between the tree graph and the non abelian loop graph contribution. An extension of our results to include non perturbative effects is possible.Comment: 15 pages, 8 figure

Novel and Unique Expression for the Radiation Reaction Force, Relevance of Newton's Third Law and Tunneling

We derive the radiation reaction by taking into account that the acceleration of the charge is caused by the interaction with some heavy source particle. In the non relativistic case this leads, in contrast to the usual approach, immediately to a result which is Galilei invariant. Simple examples show that there can be small regions of extremely low velocity where the energy requirements cannot be fulfilled, and which the charged particle can only cross by quantum mechanical tunneling. We also give the relativistic generalization which appears unique. The force is a four-vector, but only if the presence of the source is taken into account as well. It contains no third derivatives of the position as the Lorentz-Abraham-Dirac equation, and consequently no run away solutions. All examples considered so far give reasonable results.Comment: 9 page

Den Frieden abgewählt? : Die Friedenskonsolidierung in Bosnien und Herzegowina und die Wahlen im Oktober 2002

Bei den letzten Wahlen in Bosnien und Herzegowina waren die Verluste der Sozialdemokratischen Partei SDP so hoch, dass auf den meisten Ebenen eine Regierungsbildung unter Ausschluss der nationalistischen Parteien nicht mehr möglich war. Obwohl sämtliche Parteien zunächst bekräftigt hatten, dass sie Bosnien und Herzegowina als einheitlichen Staat anerkennen, kochten in der heißen Phase des Wahlkampfs wiederholt nationalistische Themen hoch. Seit dem Abkommen von Dayton wird versucht, einen sich selbst tragenden Frieden zu etablieren. Wie bei anderen Missionen der Friedenskonsolidierung galt auch in Bosnien und Herzegowina die Demokratisierung als zentrale Aufgabe. Des Weiteren wird die Einrichtung von den Volksgruppen gemeinsamen Institutionen ebenso verfolgt wie die Einführung der Gewaltenteilung, der Rechtsstaatlichkeit und eines Gewaltmonopols, das alle Bürger gleichermaßen schützt. Thorsten Gromes untersucht, wie weit die Friedenskonsolidierung gediehen ist und was der Wahlausgang für sie bedeuten kann. Er stellt drei unterschiedliche Prognosen vor, denen eines gemeinsam ist: Externe Akteure, vor allem in Gestalt des Hohen Repräsentanten, spielen weiterhin eine Schlüsselrolle. Für sie ergeben sich eine Reihe von Handlungsempfehlungen aus der jetzigen Situation. Die wichtigste davon ist, das zivile und militärische Engagement weiterzuführen, um rechtzeitig Tendenzen entgegen zu wirken, die bereits erreichte Fortschritte der Friedenskonsolidierung wieder in Frage stellen oder zunichte machen können