Foreword

Summary

For about twenty years after its invention, quantum electrodynamics remained an isolated success in the sense that the underlying ideas seemed to apply only to the electromagnetic force. In particular, its techniques did not seem to be useful in dealing with weak and strong interactions. These interactions seemed to lie outside the scope of the framework of local quantum field theory and there was a wide-spread belief that the best way to handle them would be via a more general, abstract S-matrix theory. All this changed dramatically with the discovery that non-Abelian gauge theories were renormalizable. Once the power of the gauge principle was fully recognized, local quantum field theory returned to the scene and, by now, dominates our thinking. Quantum gauge theories provide not only the most natural but also the only viable candidates we have for the description of electroweak and strong forces.

The basic dynamical variables in these theories are represented by non-Abelian connections. Since all the gauge invariant information in a connection is contained in the Wilson loops variables (i.e., traces of holonomies), it is natural to try to bring them to the forefront. This is precisely what is done in the lattice approaches which are the most successful tools we have to probe the non-perturbative features of quantum gauge theories. In the continuum, there have also been several attempts to formulate the theory in terms of Wilson loops.