Wavelet-Based Quantum Field Theory

Understand

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.