  The Euclidean quantum field theory for the fields $\phi_{\Delta x}(x)$, which
depend on both the position $x$ and the resolution $\Delta x$, constructed in
SIGMA 2 (2006), 046, hep-th/0604170, on the base of the continuous wavelet
transform, is considered. The Feynman diagrams in such a theory become finite
under the assumption there should be no scales in internal lines smaller than
the minimal of scales of external lines. This regularisation agrees with the
existing calculations of radiative corrections to the electron magnetic moment.
The transition from the newly constructed theory to a standard Euclidean field
theory is achieved by integration over the scale arguments.
