On the problem of hidden variables for quantum field theory

TL;DR

This paper argues that quantum field theory is incomplete and introduces a classical statistical model, PCSFFT, that approximates QFT averages and predicts potential deviations in future experiments.

Contribution

The paper presents PCSFFT, a classical statistical model that induces quantum field averages and reveals QFT as an asymptotic approximation.

Findings

PCSFFT reproduces QFT averages as a main term in an asymptotic expansion.

QFT predictions are approximate and may be violated in future experiments.

The Schrödinger equation of QFT emerges as a Hamilton equation in the PCSFFT framework.

Abstract

We show that QFT (as well as QM) is not a complete physical theory. We constructed a classical statistical model inducing quantum field averages. The phase space consists of square integrable functions, $f(\phi),$ of the classical bosonic field, $\phi(x).$ We call our model prequantum classical statistical field-functional theory -- PCSFFT. The correspondence between classical averages given by PCSFFT and quantum field averages given by QFT is asymptotic. The QFT-average gives the main term in the expansion of the PCSFFT-average with respect to the small parameter $\alpha$ -- dispersion of fluctuations of "vacuum field functionals.'' The Scr\"odinger equation of QFT is obtained as the Hamilton equation for functionals, $F(f),$ of classical field functions, $f(\phi).$ The main experimental prediction of PCSFFT is that QFT gives only approximative statistical predictions that might be violated in future experiments.