On the problem of hidden variables for quantum field theory

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(φ), of the classical bosonic field, φ(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 α – dispersion of fluctuations of “vacuum field functionals.” The Scrödinger equation of QFT is obtained as the Hamilton equation for functionals, F (f), of classical field functions, f(φ). The main experimental prediction of PCSFFT is that QFT gives only approximative statistical predictions that might be violated in future experiments. PACS: 03.65.Ca, 03.50.-z, 03.70.+k 1 Historical introduction on the problem of completeness of quantum theories The problem of hidden variables is closely related to the problem of completeness of quantum mechanics that was discussed in the paper