Gauge Theories and Spontaneous Symmetry Breaking.

This report summarizes attempts to understand in what way spontaneous symmetry breaking arose in the context of guage field theories of elementary particles. The main interest was in knowing whether techniques of bifurcation theory could be applied to the problem of spontaneous symmetry breaking in gauge field theories. It was felt that the symmetry breaking used by the physicists (a procedure known as the Higgs mechanism) is not precisely a bifurcation problem in the usual sense of the term, but more a matter of fixing a guage and thereby reducing the amount of symmetry of the problem. In other words, it is not really a matter of 'spontaneous' symmetry breaking.