Selfdual Gauge Field Theories

In this chapter we introduce the reader to the gauge theory formalism in order to furnish examples of gauge field theories that support a selfdual structure.

We start with the simpler abelian situation, where most of the technical aspects of group representation theory can be avoided.

From the physical point of view, an abelian gauge field theory describes electromagnetic particle interactions. Thus we shall start by discussing the abelian Maxwell– Higgs model, well-known also as the relativistic counterpart of the Ginzburg–Landau model in superconductivity (cf. [GL]). We will illustrate Bogomolnyi’s approach (cf. [Bo]) and attain selfduality for this model with parameters that describe the borderline case that distinguishes between type I and type II superconductors.