  A large mass expansion of the one-loop effective action of a scalar field on
the two-dimensional Minkowski spacetime is found in the system of coordinates,
where the metric $g_{\mu\nu}(t,x)\neq\eta_{\mu\nu}=diag(1,-1)$, and
$g_{\mu\nu}(t,x)$ tends to $\eta_{\mu\nu}$ at the spatial and temporal
infinities. It is shown that, apart from the Coleman-Weinberg potential, this
expansion contains the terms both analytic and non-analytic in $m^{-2}$, where
$m$ is the mass of a scalar field. A general unambiguous expression for the
one-loop correction to the effective action on non-stationary backgrounds is
derived.
