Classical Simulation of Quantum Fields I

Abstract

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.