A center vortex representaton of the classical SU(2) vacuum

Abstract

The classical massless SU(2) field theory has an infinite number of gauge equivalent representations of the vacuum. We show that among these there exists a non-perturbative center vortex representation with some similarity to the quantum vacuum of the same theory. This classical SU(2) vacuum consists of a lattice of center vortex pairs combining to triviality. However, this triviality can be broken by perturbations, for example by adding a mass term, or by considering the electroweak theory where the Higgs field does the breaking, or by quantum fluctuations like in QCD.