  We study classical field theories in a background field configuration where
all modes of the theory are excited, matching the zero-point energy spectrum of
quantum field theory. Our construction involves elements of a theory of
classical electrodynamics by Wheeler-Feynman and the theory of stochastic
electrodynamics of Boyer. The nonperturbative effects of interactions in these
theories can be very efficiently studied on the lattice. In $\lambda\phi^{4}$
theory in 1+1 dimensions we find results, in particular for mass
renormalization and the critical coupling for symmetry breaking, that are in
agreement with their quantum counterparts. We then study the perturbative
expansion of the $n$-point Green's functions and find a loop expansion very
similar to that of quantum field theory. When compared to the usual Feynman
rules, we find some differences associated with particular combinations of
internal lines going on-shell simultaneously.
