The gluon self-energy in cavity QCD

ANNALS

OF PHYSICS 215,

Abstracts

231-232

(1992)

of Papers to Appear in Future Issues

Algorithm for Evaluating Finite-Temperature Reaction Rates. NAOKI ASHIDA. Department of Physics, Osaka City University, Sumiyoshi-ku, Osaka 558, Japan; HISAO NAKKAGAWA AND AKIRA NIBGAWA. Fakultlt fur Physik, UniversitLt Bielefeld, D-4800 Bielefeld, Germany; AND HIROSHI YOKOTA. Institute for Natural Science, Nara University, 1500 Misasagi-cho, Nara 631, Japan.

Diagrammatic

In this paper, by following the procedure of statistical mechanics we present the systematic calculational rules for evaluating the reaction rate of a generic dynamical process taking place in a heat bath. These rules are formulated within the framework of real-time thermal field theory (RTFT), in terms of the Feynman-like diagrams, the so-called circled diagrams. With the machinery developed in this paper we can establish the finite temperature generalization of the Cutkosky, or the cutting rules in quantum field theory at zero temperature. We have also studied the relation between the imaginary part of forward RTFT amplitude and the reaction rates; the imaginary part consists of various reaction rates. This is a finite temperature generalization of the optical theorem.

Tire Gluon Self-Energy itl Cavify QCrt. G. U. SCHREIBERAND R. D. VIOLLIER. Institute of Theoretical Physics and Astrophysics, University of Cape Town, Rondebosch 7700, South Africa. A numerical technique to regularize divergent loop diagrams in cavity QCD is discussed, which is closely related to dimensional regularization in free space. In this cavity regularization method, the energy shift is expressed as the integral of a divergent spectral function, from which the divergence may be extracted using the analytical free space expression. The technique is used to evaluate the self-energy of the low-lying gluon modes in a cavity. The values of the vacuum polarization turn out to be positive for both the quark and the gauge loops.

Dyson’s Equations Matter. K.

for

Nucleon-Pion-Delta

Interactions:

Toward

a Self-Consistent

Solution

in Nuclear

T. R. DAVIES. Center for Computationally Intensive Physics, Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6373.

A formalism is developed for the self-consistent solution of Dyson’s equations for the pion and the delta in cold nuclear matter. The nucleondelta and nucleon-pion “loop integrals” are evaluated and are inserted into the pion and delta-particle propagators, respectively. The resulting pion propagator displays two distinct families of “spikes” which are dramatically different from the free-space behavior. In particular, there are significant high-momentum components of the pion which give large contributions to the nucleon-pion loop integral. Such contributions lead to severe spikes in the iterated delta propagator. Studies are made too of the sensitivity of the results of the cutoff range of the “form factor” used to evaluate the loop integrals, to the starting solution, and to the density. Also, for the densities studied here, the pion propagator exhibits pure delta-function singularities, which occur over a small range of energies just above the mass of the pion. However, it is shown that such delta functions have a negligible effect on the main calculation. Finally, this paper gives a comprehensice treatment of the main methods used to solve the nuclear matter Dyson’s equations.

231 0003-4916192 $7.50 Copyright 0 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.