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

TL;DR

This paper proposes a novel way to express quantum field theory using two classical fields in ordinary space with an extra dimension, aiming to bridge quantum and classical descriptions.

Contribution

It introduces a new classical field-based formulation of QFT with a single extra dimension, enabling a coarse-grained approximation of quantum states.

Findings

Provides a classical field model for QFT in one extra dimension

Models ensemble of states with a single classical state

Maintains non-locality in the classical formulation

Abstract

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.