ABSTRACT
One of the more puzzling features of contemporary relativistic quantum mechanics is the enforced retreat into the concepts of ‘external’ and ‘internal’ spaces that are locally independent. Here the elementary particles are not thought of as extended structures in space-time but are regarded primarly as point objects with ‘internal’ variables such as spin, isospin, hypercharge, charm, etc., together with the usual ‘external’ space-time properties like momentum, mass, etc. This way of proceeding seems inescapable and is forced on us, not so much by physical considerations, but by technical difficulties arising from the mathematics itself. Nevertheless, this approach has received considerable impetus with the realisation that the mathematical theory of fibre bundles, a theory developed for very different reasons, provides a natural descriptive language for these ideas.
