Applications and methods of group theory in elementary particle physics

The use of Schur function methods in the evaluation of Kronecker products of irreducible representations of the compact semisimple Lie groups is reviewed. For irreducible representations of the classical groups, explicit, unambiguous and rank-independent general formulae are derived. In particular, for the group SO₂k, a technique necessitating the derivation of new branching rules is used to obtain the appropriate formulae. The same technique is used to obtain efficient methods for the evaluation of Kronecker products of the irreducible representations of the exceptional groups. An account is given on computer algorithms developed to implement these methods and formulae. Tensor operator methods are used to evaluate colour-spin matrix elements of the multiquark hadrons q³q-³. The static spherical cavity approximation to the MIT bag model is used to calculate the masses of the S-wave q³q-³ states. Many of these states are found to have masses below the baryon-antibaryon threshold, but none are found below the triple meson threshold. Dissociation calculations are performed on the states which have nucleon-antinucleon content. Some comments concerning the relationship of the states to experiment are made