Abstract:
It is proved that the perturbation theory series in translation-invariant case and
with the removed cut-off of boson propagator for the euclidean Green functions; converges
if $|g|^2/\bar m\lambda^2/96\bar\Delta(0)$. Here $\bar m$ is a certain quantity which remains finite when the
fermion propagator regularization is removed, $\lambda^2$ is the boson mass and $\bar\Delta(0)$ is the value of the fermion propagator at the point $x=0$ of the $x$-space. By means of other methods the same problem was considered in the work [6] for the pseudo-euclidean and
in the work [5] for the euclidean Green functions.
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