Adventures in Coulomb Gauge.pdf

a r X i v : h e p - l a t / 0 3 0 9 1 7 2 v 1 2 6 S e p 2 0 0 3 February 1, 2008 4:19 WSPC/Trim Size: 9in x 6in for Proceedings conf2003 ADVENTURES IN COULOMB GAUGE ?? JEFF GREENSITE Physics and Astronomy Dept., San Francisco State University, San Francisco, CA 94117. E-mail: greensit@stars.sfsu.edu S?TEFAN OLEJNI?K Institute of Physics, Slovak Academy of Sciences, SK-845 11 Bratislava, Slovakia. E-mail: fyziolej@savba.sk We study the phase structure of SU(2) gauge theories at zero and high temperature, with and without scalar matter fields, in terms of the symmetric/broken realization of the remnant gauge symmetry which exists after fixing to Coulomb gauge. The symmetric realization is associated with a linearly rising color Coulomb potential (which we compute numerically), and is a necessary but not sufficient condition for confinement. There are several reasons why Coulomb gauge may be interesting and/or useful in the study of the confining force. First of all there is the speculation by Gribov [1] and Zwanziger [2] that confinement in Coulomb gauge is due to instantaneous (dressed) one-gluon exchange. Secondly, the behavior of the color Coulomb potential, defined in Coulomb gauge, is an important element in the gluon-chain model of QCD string formation [3]. Finally, as we will see below, the confining property of the color Coulomb potential is associated with the unbroken realization of a remnant gauge symmetry, and this suggests a new order parameter for studying the phase structure of lattice gauge theories. We begin with the idea that confinement arises from one-gluon exchange in Coulomb gauge; specifically, from the instantaneous piece of the 〈A0A0〉 propagator 〈Aa0(x)A b 0(y)〉 = P (~x? ~y)δ abδ(x0 ? y0) + non-instantaneous (1) ?Talk presented by J. Greensite at Confinement 2003, Tokyo, July 21-24. ?Work supported by the US Dept. of Energy, Grant No. DE-FG03-92ER40711 (J.G.), and the Slovak Grant Agency for Science, Grant No. 2/3106/2003 (S?.O.) 1 Februa