  Solutions of the classical $\phi^4$-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.
