Quasiclassical expansion of the Euclidean $P(\varphi)_2$ model

A complete quasiclassical expansion of the Euclidean $P(\varphi)_2$ model of quantum field theory with source is obtained. In particular, it is shown that the expectation value of the Euclidean field satisfies $\langle\Phi(x)\rangle_h\to u(x)$ as $h\to 0$ where $u(x)$, a classical field, is a solution of the equation $\Delta u-m^2u=P'(u)-f(x)$.