The main purpose of this monograph is the presentation of certain classes of exact solutions of the Yang-Mills field equations, together with classification schemes for these solutions. A second objective is a detailed analysis of the motion of a test particle in some classical gauge fields. In the opening chapter the SU(2) Yang-Mills field equations in flat space-time are briefly introduced in accordance with standard procedures. These equations are then reformulated in terms of the null-tetrad formalism since the latter gives rise to new exact solutions. In the next chapter three classification methods are presented. The first of these is based on the various eigenspinors and eigenvalues that describe the fields, while the second involves the rank of the matrix $E+iH$, where E and H respectively denote the electric and magnetic parts of the fields. In the third method the fields are classified by means of the little group that leaves these fields invariant. This is followed by a chapter on static solutions of sourceless Yang-Mills field equations with particular emphasis on two exact solutions that may coincide under certain circumstances. Further exact solutions are derived by means of some of the aforementioned classification schemes, much of this analysis being carried out in terms of the null-tetrad formalism. A substantial chapter is devoted to an analysis of the problem of the motion of a test particle in classical gauge fields for two distinct cases. The first of these is based on the magnetic solution that had been derived previously, while the second analysis is carried out within the context of an instanton field. The resulting equations of motion assume a rather complicated form in both cases. Although this is not stated explicitly, it would appear that the book presupposes some background knowledge of the theory of gauge fields on the part of the reader. However, for the specialist this monograph contains a wealth of significant information.
H.Rund (Tucson)