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Approaching quantum behavior with classical fields

By averaging over an ensemble of field configurations, a classical field theory can display many of the characteristics of quantum field theory, including Lorentz invariance, a loop expansion, and renormalization effects. There is additional freedom in how the ensemble is chosen. When the field mode amplitudes have a Gaussian distribution, and the mode phases are randomly distributed, we review the known differences between the classical and quantum theories. When the mode amplitudes are fixed, or have a nongaussian distribution, the quartic and higher correlations among the free fields are modified, seemingly in a nonlocal way. We show how this in turn affects the perturbative expansion. We focus on $λϕ^4$ theory in 1+1 dimensions and use lattice simulations to augment our study. We give examples of how these nonlocal correlations induce behavior more similar to quantum field theory, at both weak and strong coupling.