Bosonic loop diagrams as perturbative solutions of the classical field equations in 4-theory

Abstract

Solutions of the classical �4-theory in Minkowski space-time are analyzed
in a perturbation expansion in the nonlinearity. Using the language of Feynman
diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams
which involve the retarded Green’s function and have one outgoing leg. In order to
obtain general tree diagrams, we set up a “classical measurement process” in which
a virtual observer of a scattering experiment modifies the field and detects suitable
energy differences. By adding a classical stochastic background field, we even obtain
all loop diagrams. The expansions are compared with the standard Feynman
diagrams of the corresponding quantum field theory.