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.
The goal of this paper is to reduce many body quantum mechanics to single particle one in
R5. This is done by treating
x5 coordinate as filling curve that would fill configuration space up to some coarse graining. After working it out for the case of many body QM, this idea is then extended to QFT.