Introduction

The discovery of such a wealth of apparently ‘elementary’ particles stimulated new activity in the search for a pattern amongst them, as a first step towards the understanding of their nature. The discovery of such a pattern is analogous to, for instance, the discovery of the Rydberg formula in atomic spectroscopy. The Bohr atom finally provided an explanation of the formula, and we shall see that the quark model provides an explanation of the symmetry pattern of the elementary particles.

We have already become familiar with the limited symmetry of isotopic spin multiplets. In that case we grouped together particles which were the same except for properties associated with the electric charge. The degeneracy of the multiplet is removed by the symmetry-breaking Coulomb interaction. Alternatively, we can regard the members of the multiplet as states linked by rotations in isotopic spin space and we can define a group of rotation operators which enable us to step from one state to another.

The Coulomb interaction is not strong compared with the so called ‘strong’ interactions, and the symmetry breaking to which it gives rise is small. For instance, the masses of particles in the same isotopic spin multiplet differ only by at most a few per cent. In order to extend the symmetry, to group larger numbers of particles together, we must recognise the existence of much stronger symmetry breaking forces since the mass differences between, say, I-spin multiplets, are substantial, even compared with the particle masses themselves.