The Berry phase and monopoles in gluodynamics

Abstract

We introduce a gauge invariant definition of a monopole on the lattice. The construction is based on the observation that for each Wilson loop there exists an extra U(1) group which leaves the loop invariant. Since the lattice formulation utilizes the language of Wilson loops, the definition of the monopole charge in terms of this plaquette dependent U(1) is gauge invariant. The explicit construction of gauge invariant monopoles is presented both in continuum and on the lattice.