ABSTRACT

This chapter restricts attention to massless spin 1 particles. The reason for this is that it turns out for the non-Abelian case (Yang–Mills theories) that renormalisability of the field theory requires the vector fields to be massless in the first instance. The masses of the vector fields are generated at a later stage through certain scalar fields (Higgs scalars) acquiring vacuum expectation values. The earliest field theory involving massless vector fields is quantum electrodynamics, the theory of the electromagnetic interactions of particles. The chapter derives a gauge invariant Lagrangian using a principle called gauge invariance. It describes non-Abelian gauge field theories and derives field equations for gauge field theories.