  We construct the solution $\phi(t,{\bf x})$ of the quantum wave equation
$\Box\phi + m^2\phi + \lambda:\!\!\phi^3\!\!: = 0$ as a bilinear form which can
be expanded over Wick polynomials of the free $in$-field, and where
$:\!\phi^3(t,{\bf x})\!: $ is defined as the normal ordered product with
respect to the free $in$-field. The constructed solution is correctly defined
as a bilinear form on $D_{\theta}\times D_{\theta}$, where $D_{\theta}$ is a
dense linear subspace in the Fock space of the free $in$-field. On
$D_{\theta}\times D_{\theta}$ the diagonal Wick symbol of this bilinear form
satisfies the nonlinear classical wave equation.

High Energy Physics - Theory