Hamilton approach to Yang-Mills theory in Coulomb gauge

Abstract

SUMMARY AND CONCLUSIONS In my talk I have discussed recent results obtained in the Hamilton approach to Yang-Mills theory in Coulomb gauge. Using ghost dominance, an infrared analysis of theSchwinger-Dyson equations has revealed both quark and gluon confinement. The gluonenergy is infrared diverging implying the absence of asymptotic gluon states from thephysical spectrum, and the static Coulomb potential is linearly rising. These results areconfirmed by a full numerical solution of the Schwinger-Dyson equations. While theghost-gluon vertex remains basically unrenormalized and in particular becomes the bareone when the ghost momentum vanishes, the three-gluon vertex is strongly infrareddivergent. As a first non-trivial test of the variationally determined vacuum wave func-tional, we have calculated ’t Hooft’s disorder parameter choosing the renormalizationconstants of the gap equation in such a way that the wave functional reproduces in theinfrared the strong coupling limit. Then the ’t Hooft loop shows indeed a perimeter law,indicating a confining vacuum.