The Quantum Theory of Free Fields
The canonical quantization of the free, real scalar field. Difficulties with the Schroedinger representation. Inequivalent representations of the canonical commutation relations. The Fock representation. Basic quantum observables: the total energy and momentum of the field. A description of quantum states in terms of particles. The field operator as a generalized function. The classical Dirac field as a system with constraints. The Faddeev–Jackiw method and quantization of the free Dirac field. The Dirac vacuum and the appearance of a free, relativistic, spin 1/2 particle and its antiparticle. Extraction of the physical degrees of freedom of the free electromagnetic field. The canonical quantization of the electromagnetic field and the appearance of a free, massless particle (the photon).