Applications of the Theory of Continuous Groups

Abstract

In the following we discuss some applications of the theory of continuous groups, but without being complete and exhaustive. It is our aim just to illustrate the possibilities of the theory with some examples. We cannot give a complete discussion of all symmetry groups used in modern particle physics. Rather, we show with some examples how to employ some groups, ℒ U n ⩽5, in modern physics and how to work with mechanisms of symmetry breaking. The methods given can also be transferred to an investigation of higher and supersymmetries and more fundamental (?) particles (i.e. partons, rishons, haplons and preons). We assume the physical foundations essentially to be known.