Quantized Fields and their Interpretation

Abstract

This chapter deals with the quantum theory of systems with an infinite number of degrees of freedom and provides elements of quantum field theory. A classical field such as the real scalar field, a Maxwell field, or some continuous mechanical system, when subject to the rules of quantum theory, turns into a field operator which can create or annihilate quanta of this field and which describes the kinematics and the spin properties of these quanta. This step allows to extend scattering theory to processes in which quanta, or particles, are created or annihilated, and, thus, which do not necessarily conserve particle numbers. Canonical quantization is based on a formalism making use of Lagrange densities which are constructed in view of a mild generalization of Hamilton’s variational principle of point mechanics. Hence, it is not difficult to build in, or take care of, symmetries and invariances of the theory. In particular, creation and annihilation of particles by interaction terms which determine reactions and decay processes, will always be in accord with the selection rules of the theory.