  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 the
first classical field is to set up an injection from the set of values of extra
dimension into the set of functions, and then said injection will be used in
order to convert the second field into a coarse grained functional, thereby
approximating QFT state. It turns out that this work also has a side-benefit of
modeling ensemble of states in terms of one single state which, in turn, is
interpretted in the above way. It is important to clarify that by "classical"
we mean functions over ordinary space rather than configuration, Fock or
function space. The "classical" theory that we propose is still non-local.
