Nonlocal stochastic model for the free scalar field theory

The free scalar field is investigated within the framework of the Davidson stochastic model and of the hypothesis on space-time stochasticity. It is shown that the resulting Markov field obtained by averaging in this space-time is equivalent to a nonlocal Euclidean Markov field with the times scaled by a common factor which depends on the diffusion parameter. Our result generalizes Guerra and Ruggiero's procedure of stochastic quantization of scalar fields. On the basis of the assumption about unobservability of in quantum field theory, the Efimov nonlocal theory is obtained from Euclidean Markov field with form factors of the class of entire analytical functions.