ABSTRACT
The relativistic wave equations and eld theories we encountered in Chapter 7 described only the properties of free, non-interacting particles. The wave equation for a free particle is always of the form (dierential operator) = 0, and therefore the corresponding Lagrangians are quadratic in the elds. We have already seen that gauge theories give rise, in a natural way, to Lagrangians that contain terms of higher than quadratic order in the elds, and these terms describe interactions. In (8.41), for example, /A describes an interaction between a fermion and a gauge eld, while the higher-order terms in F aF
a describe interactions of the gauge elds amongst themselves. It is, of course, only in the presence of interactions that physically interesting events can occur.
