**Wavelet-based quantum field theory**

**Abstract:**

We construct a Euclidean field theory for the fields φ_{Δx}(*x*) that
depend on both position and resolution. The Feynman diagrams
in such theory become finite under the assumption that there
should be no scales in internal lines smaller than the minimal
of scales of external lines. The construction is performed using
the continuous wavelet transform with the basic wavelet being
understood as an apparatus function of an abstract measuring
device. The transition from the newly constructed theory to a
standard Euclidean field theory is achieved by integration over
the scale arguments and shows that the source of divergences
in standard theory is the integration over all scales which is
unfeasible for it would require infinitely high energies.