Quantum field theory as a bilocal statistical field theory

We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be treated similar to the usual formalism. Situations where the formalism can be interpreted in terms of a statistical field theory in Minkowski space are characterized by violations of unitarity at very large momentum scales. Renormalization group equations suggest that unitarity can be essentially restored by strong fluctuation effects.