The stationary states of interacting fields

Abstract

As an application of a time-independent perturbation formalism developed earlier for systems with many degrees of freedom, we give in terms of diagrams the general perturbation expressions for the exact stationary states of interacting fields. The physical vacuum is obtained by applying to the bare vacuum the exponential of an operator simply expressed in terms of connected diagrams. For the states with one or more physical particles expressions are found in the form of suitably defined creation operators applied to the physical vacuum. The incoming and outgoing parts of a scattering state are analyzed in terms of products of physical particle creation operators, the connection being given by the S-matrix. Some remarks are made on renormalization. For electrodynamics in particular the ratio of renormalized to unrenormalized fine structure constants is shown to have a simple probabilistic interpretation: it is the probability to find the bare one-photon state in the physical one-photon state of vanishing momentum, divided by the probability to find the bare vacuum in the physical vacuum.