  With the help of the complex structure and the wave operator of the nonlinear
classical Klein-Gordon equation with the interaction $u^4_4$ we define the Wick
kernel of the interacting quantum field in four-dimensional space-time and
consider its properties. In particular, the diagonal of this Wick kernel is
(real) solutions of the classical nonlinear Klein-Gordon equation with the
interaction $u^4_4.$
