Broken Symmetry

Abstract

This chapter describes the broken symmetry groups of elementary particle physics, namely, SU (3) and SU (6), from a general and elementary point of view. It focuses on real connected simple compact Lie groups. Real Lie groups are defined in the usual way as the groups whose elements are describable by a finite number of real parameters, each of which can have a continuous range of values. A connected Lie group means a group, all of whose elements can be reached by proceeding continuously from the identity, that is, by letting the parameters vary continuously from zero. The simple Lie groups are those that contain no invariant Abelian subgroups. An example of a real connected simple compact Lie group is the rotation group in three dimensions. The parameters in this case are the Euler angles, which are real and have ranges [0, 2π[ and [0, π[. If the space reflections are included, the group loses its connectivity. An example of a non-compact group is the inhomogeneous Lorentz group, for which the parameters of acceleration range from –∞ to ∞. The chapter also discusses the use of the Wigner–Eckart (W–E) Theorem in deducing the experimental consequences of broken symmetry and the application of the theorem to the broken symmetry group SU(3).