ABSTRACT
Particle physics is formulated using the language of relativistic quantum field theory. This chapter addresses ourselves first to the derivation of the principal results of classical (i.e. non-quantum) field theory. A field is a generalisation of the notion of a generalised coordinate, not just to several particles, but to a continuum of particles, with the possibility of one or more at each point in space. One of the advantages of the Lagrangian formulation is that it permits the ready identification of conserved quantities by studying the invariances of the action S. The fundamental result behind this statement is Noether’s theorem, which identifies the conserved current associated with the invariance of S under a very general infinitesimal transformation. The generalisation of spinor field theory to a quantum field theory will require functional integration over classical spinor field configurations. Neutrinos are observed only in a left-handed helicity state; the right-handed neutrino state, even if it exists, is not observed in weak processes.
