ABSTRACT
The key task from a theoretical viewpoint is to compute the matrix element for a given process. However, before trying to evaluate “real-world” processes such as those that occur in Quantum Electrodynamics or Quantum Chromodynamics, it’s useful to look at what physicists call a "toy"-theory: a theory that is not necessarily intended to model the real world but whose purpose is to illustrate the essential features of the method. Spin is an essential feature of the real world but unfortunately its inclusion leads to a fair amount of messy algebra when calculating cross sections, decay rates, etc. Non-renormalizable theories do not have this feature – they have an infinite number of infinities, and so yield meaningless results. It would be nice if we could just ignore these kinds of theories, but we can’t – it turns out that our best theory of gravity – general relativity – is a non-renormalizable theory.
