ABSTRACT
This chapter contains a brief compilation of information about various fields and contractions. The field formalism is fully applicable also to the ordinary quantum mechanics of systems with a finite number of degrees of freedom. The simplest example is that of a particle in a given external field. Preliminary separation of the δ function is necessary, for example, when calculating the amplitude by the stationary-phase method (the semiclassical approximation), since the conservation laws expressed by the δ functions automatically make the kernel of the quadratic form of the second variation of the action degenerate in the neighborhood of a classical trajectory. Nonrelativistic field theory is the quantum mechanics of systems with an arbitrary number of identical particles in the second-quantized formalism. In the classical theory such systems are described by a complex field ψ, ψ+ which is an ordinary or anticommuting function.
