Starting from the notion of path integrals as developed by Feynman, we discuss field theory in zero space-time dimensions. The concepts of perturbation expansions, connected amplitudes, Feynman diagrams, classical solutions, renormalization and the effective action are developed. The model is extended to four space-time dimensions, and the full Feynman rules for relativistic scalar theory derived.
The S matrix and the concept of unitarity are discussed, leading
to the amputation rules for S matrix elements from considerations of unitarity. The rules are extended to include particles with spin-1/2 and spin-1. The high-energy behaviour of the theory is discussed as a method to derive the gauge symmetry of the various models.