TY - JOUR

T1 - Confinement made simple in the Coulomb gauge

AU - Cucchieri, Attilio

AU - Zwanziger, Daniel

N1 - Funding Information:
A particularly simple confinement scenario \[1,2\] is available in the minimal Coulomb gauge 1. It attributes confinement of color to the enhancement at long range of the color-Coulomb po- *Talk presented by D. Zwanziger tResearch partially supported by FAPESP, Brazil (Project No. 00/05047-5). E-mail address: attilio~if.sc.usp.br tResearch partially supported by the National Science Foundation, grant no. PHY-0099393. E-mail address: daniel.zwanziger@nyu.edu 1The minimal lattice Coulomb gauge is obtained by first minimizing -~-~.z,i=lTrgUx,i 3 with respect to all local gauge transformations g(x), and then minimizing - ~x TrgUx,4 with respect to all x-independent but x4-dependent gauge transformations g(x4). This makes the 3-vector potential Ai, for i ----1 , 2, 3 transverse, OiAi = O, so Ai -----A ~r . Moreover, the Coulomb gauge is the finite limit of renormalizable gauges \[3\].

PY - 2002/3

Y1 - 2002/3

N2 - In Gribov's scenario in Coulomb gauge, confinement of color charge is due to a long-range instantaneous color-Coulomb potential V(R). This may be determined numerically from the instantaneous part of the gluon propagator D44,inst = V(R)δ(t). Confinement of gluons is reflected in the vanishing at k = 0 of the equal-time three- dimensionally transverse would-be physical gluon propagator Dtr(k). We present exact analytic results on D44 and Dtr (which have also been investigated numerically, A. Cucchieri, T. Mendes, and D. Zwanziger, this conference), in particular the vanishing of Dtr(k) at k = 0, and the determination of the running coupling constant from χ0g2(k) = k2 D44,inst, where χ0 = 12N/(11N - 2Nf).

AB - In Gribov's scenario in Coulomb gauge, confinement of color charge is due to a long-range instantaneous color-Coulomb potential V(R). This may be determined numerically from the instantaneous part of the gluon propagator D44,inst = V(R)δ(t). Confinement of gluons is reflected in the vanishing at k = 0 of the equal-time three- dimensionally transverse would-be physical gluon propagator Dtr(k). We present exact analytic results on D44 and Dtr (which have also been investigated numerically, A. Cucchieri, T. Mendes, and D. Zwanziger, this conference), in particular the vanishing of Dtr(k) at k = 0, and the determination of the running coupling constant from χ0g2(k) = k2 D44,inst, where χ0 = 12N/(11N - 2Nf).

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U2 - 10.1016/S0920-5632(01)01819-9

DO - 10.1016/S0920-5632(01)01819-9

M3 - Article

AN - SCOPUS:0036524996

VL - 106-107

SP - 694

EP - 696

JO - Nuclear and Particle Physics Proceedings

JF - Nuclear and Particle Physics Proceedings

SN - 2405-6014

ER -