4 Abelian Gauge Fixing

Abstract

The formation of monopoles and their condensation in the QCD ground state is a feature which is related to abelian gauge fixing, discussed in this chapter. The gluon field acquires a singularity in the vicinity of points in space where abelian gauge fixing fails and magnetic monopoles are formed there. The ideas discussed in this chapter can be found in the 1974 and 1981 seminal papers of Polyakov [9] and ‘t Hooft [92, 93]. It is also very instructive to read the Sect. 23.3 (vol. 2) of Weinberg’s Quantum Theory of Fields [55]. The formation of monopoles in QCD is still a subject of occasional debate [94, 95] The choice of the abelian gauge is, of course, not unique, and nor is the corresponding definition of the monopoles. However, lattice calculation performed by the Pisa group [19, 20, 21, 25] suggest that the condensation of monopoles in the QCD ground state is remarkably independent of the gauge fixing condition. The recent gauge invariant definition of monopoles, proposed by Gubarev and Zakharov [96, 97], is not discussed in these lectures.