EDGE STATES IN GAUGE-THEORIES - THEORY, INTERPRETATIONS AND PREDICTIONS

Gauge theories on manifolds with spatial boundaries are studied. It is shown that observables localized at the boundaries (edge observables) can occur in such models irrespective of the dimensionality of space- time. The intimate connection of these observables to charge fractiona tion, vertex operators and topological field theories is described. Th e edge observables, however, may or may not exist as well-defined oper ators in a fully quantized theory depending on the boundary conditions imposed on the fields and their momenta. The latter are obtained by r equiring the Hamiltonian of the theory to be self-adjoint and positive -definite. We show that these boundary conditions can also have nice p hysical interpretations in terms of certain experimental parameters, s uch as the penetration depth of the electromagnetic field in a surroun ding superconducting medium. The dependence of the spectrum on one suc h parameter is explicitly exhibited for the Higgs model on a spatial d isk in its London limit. It should be possible to test such dependence s experimentally, the above Higgs model for example being a model for a superconductor. Boundary conditions for the (3 + 1)-dimensional BF s ystem confined to a spatial ball are studied. Their physical meaning i s clarified and their influence on the edge states of this system (kno wn to exist under certain conditions) is discussed. It is pointed out that edge states occur for topological solitons of gauge theories such as the 't Hooft-Polyakov monopoles.