ANNALS OF PHYSICS 190, 373427 (1989) Linear Response of Hot Gluons* M. E. CARRINGTON, T. H. HANSON, H. YAMAGISHI, AND I. ZAHED Physics Department, State University of New York, Stony Brook, New York, 11794 Received June 14, 1988; revised October 31, 1988 We reexamine the various schemes for calculating the linear response (the retarded Green’s function) of a hot gluon plasma. The problems related to gauge invariance are discussed in detail, and results in different gauges are compared. We also point out some issues related to the very definition of a thermal ensemble in the presence of unphysical degrees of freedom. By calculating the retarded Green’s function directly in real time, we explicitly study the effectsof unphysical degrees of freedom in different gauges. Although there appears to be no unique way to define the response function, we find that several schemes can be questioned on formal grounds and that use of the background-field gauge (BFG) is the most satisfactory in this respect. We discuss two proposals to fix the gauge parameter (a) dependence in the BFG response function, the Vilkovisky-Dewitt effective action corresponding to the choice a = 0 (background Landau gauge), and the “gauge-invariant propagator” of Cornwall et al. corresponding to m = 1 (background Feynman gauge). 8 1989 Academic Press, Inc. 1. INTRODUCTION The possibility of creating and probing quark-gluon plasmas in relativistic heavy ion collisions has greatly spurred the efforts to understand QCD at high tem- peratures and densities. The vast literature on the subject covers aspects ranging from straightforward reaction kinematics to speculations about the nonperturbative aspects of the QCD high temperature phase. The techniques employed include those of nuclear many-body theory, relativistic transport theory, bootstrap and duality, perturbative QCD, string-based hadronization models, and lattice Monte Carlo simulations. ’ Assuming that a quark-gluon plasma can be formed, one may ask how it can be detected, and how one will probe its properties. These are crucial questions which must be answered, if the planned experiments are to provide new insights into the physics of hadrons and the structure of QCD. Many signatures of the plasma state have been proposed, e.g., enhanced strangeness production, increased transverse energy flow, and shift, broadening, and disappearance of resonance peaks. Another line of development involves the study of various correlation functions * Supported in part by the U.S. Department of Energy under Grant DE-FG02-88ER40388. ’ Even the literature on tinite T perturbative QCD is already extensive, and we will not give a complete bibliography but refer to the reviews [l-3 3. 373 0003-4916/89 $7.50 Copyright 0 1989 by Academic Press, Inc. All rights of reproductmn in any form reserved.