Classical nonlocal models for states of the quantized real Klein-Gordon field

Classical nonlocal field models consisting of probability densities over functions defined everywhere on Minkowski space are constructed, using functional methods. These models are equivalent to states of the quantized real Klein-Gordon field in the sense that the marginal probability density over real functions defined everywhere on a 3dimensional hyperplane S, at all times and for all Lorentz boosts, is equal to the corresponding probability density over real functions on S that is given by a state of the quantized real Klein-Gordon field. This paper establishes a relationship between quantum field theory and classical statistical field theory different from the well-known relationship of analytic continuation.