  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.
