Wavelet-Based Quantum Field Theory

The Euclidean quantum field theory for the fields ${\varphi }_{\mathrm{\Delta }x}(x)$, which depend on both the position $x$ and the resolution $\mathrm{\Delta }x$, 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.