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A large mass expansion of the one-loop effective action of a scalar field onthe 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 temporalinfinities. It is shown that, apart from the Coleman-Weinberg potential, thisexpansion 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 theone-loop correction to the effective action on non-stationary backgrounds isderived.

Large mass expansion of the one-loop effective action induced by a  scalar field on the two-dimensional Minkowski background with non-trivial  $(1+1)$ splitting