Interacting Fields

We present a simple form of the Wightman axioms in a four-dimensional Minkowski space-time which are supposed to define a physically interesting interacting quantum field theory. Two important consequences follow from these axioms. The first is the invariance under CPT which implies, in particular, the equality of masses and lifetimes for particles and anti-particles. The second is the connection between spin and statistics. We give examples of interacting field theories and develop the perturbation expansion for Green functions. We derive the Feynman rules, both in configuration and in momentum space, for some simple interacting theories. The rules are unambiguous and allow, in principle, to compute any Green function at any order in perturbation.