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The goal of this paper is to re-express QFT in terms of two "classical"fields living in ordinary space with single extra dimension. The role of thefirst classical field is to set up an injection from the set of values of extradimension into the set of functions, and then said injection will be used inorder to convert the second field into a coarse grained functional, therebyapproximating QFT state. It turns out that this work also has a side-benefit ofmodeling ensemble of states in terms of one single state which, in turn, isinterpretted in the above way. It is important to clarify that by "classical"we mean functions over ordinary space rather than configuration, Fock orfunction space. The "classical" theory that we propose is still non-local.

Expressing QFT in terms of QM with single extra dimension and classical hidden variable field