Group Theory and Its Applications

The application of group theory can be subdivided generally into two broad areas: one, where the underlying dynamical laws (of interactions) and therefore all the resulting symmetries are known exactly; the other, where these are as yet unknown and onlt the kinematical symmetries (i.e., those of the underlying space-time continuum) can serve as a certain guide. In the first area, group theoretical techniques are used essentially to exploit the known symmetrics, either to simplify numerical calculations or to draw exact, qualitative conclusions. In the second major area, application of group theory proceeds essentially in the opposite direction. In part as a consequence of these developments, physical scientists have been forced to concern themselves more profoundly with mathematical aspects of the theory of groups that previously could be left aside; Questions of topology, representations noncompact groups, more powerful methods for generating representations, as well as a systematic study of Lie groups and the algebras, in general belong in this category. This volume, as did the earlier ones, contains contributions in all these areas.The coverage of subjects of applied group theory is still neither complete nor completely balanced, though it is more so than it was in Volume I and II. To a large extent this is inevitable in a filed growing and evolving as rapidly as this one.