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 $\lambda {\varphi }^4$ 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.

21 pages, 7 figures, now matches published version

References in corpus (7)

• Classical decay of inflaton
• Finiteness of Hot Classical Scalar Field Theory and the Plasmon Damping Rate
• The Boltzmann Equation in Classical and Quantum Field Theory
• Monte Carlo Simulation Calculation of Critical Coupling Constant for Continuum ϕ^4_2
• Staying Thermal with Hartree Ensemble Approximations
• Fluctuations, Ghosts, and the Cosmological Constant
• Approaching quantum behavior with classical fields

Cited by in corpus (2)

• Quantum and Classical Behavior in Interacting Bosonic Systems
• Classical Statistical simulation of Quantum Field Theory