Geometry of Yang–Mills A-Connections

Abstract

The geometry referred to in the title concerns an application of classical differentialgeometric notions/methods in the study of structure properties (geometry) of the space that interests us here, which is the space of solutions (again!) of the so-called Yang–Mills equations; these solutions are, by definition, A-connections in the sense of the present treatise, which thus appear on the stage through their corresponding curvature (field strength), which is actually involved in the equations at issue. (See also Chapter I, Section 4, for the precise terminology employed.) On the other hand, since, by virtue of their own nature, the objects concerned (A-connections solutions) are not distinguished insofar as they are “gauge equivalent;” one is led to consider not the initial solution space, as above, but, in effect, an appropriate “quotient” of it—the so-called “moduli space” of the solutions (A-connections) under consideration.