Our principal aim in this chapter is to review briefly the basic ideas of field theory, which we shall illustrate with examples from quantum electrodynamics (QED) and the theory of strong interactions, quantum chromodynamics (QCD). Of necessity, we must assume that the reader has some knowledge of field theory and is conversant with the idea of Feynman diagrams and with the Dirac equation. We shall then give a resumé of the theory and phenomenology of the weak interactions as they stood at the time of the inception of the new ideas about quarks and gluons in the early 1970s. The chapter ends with some technical results which will be very useful in later chapters.

The detailed rules for the Feynman diagrams for the various field theories are given in Appendix 2.

A brief introduction to field theory

Processes in which particles can be created or annihilated are best treated in the language of quantum field theory, using field operators ø(x) that are linear superpositions of operators a†(p) and a(p) which respectively create and annihilate particles of momentum p when they act upon any state vector. If the state happens not to contain the relevant particle of momentum p then a(p) acting on it just gives zero (the detailed mathematical relationship can be found in Appendix 1).