New Interpretation of the Euclidean-Markov Field in the Framework of Physical Minkowski Space-Time

The Euclidean-Markov field, extensively used in constructive quantum field theory, is shown to be the same as the lowest energy generalized stochastic process associated with classical field theory through the procedure of Nelson's stochastic mechanics. As a result, the underlying four-dimensional manifold, on which the Markov field is defined, can be considered as the physical space-time.