
SIGMA 3 (2007), 105, 13 pages arXiv:0711.1671
http://dx.doi.org/10.3842/SIGMA.2007.105
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics
WaveletBased Quantum Field Theory
Mikhail V. Altaisky ^{a, b}
^{a)} Joint Institute for Nuclear Research, Dubna, 141980, Russia
^{b)} Space Research Institute RAS, 84/32 Profsoyuznaya Str., Moscow, 117997, Russia
Received August 15, 2007, in final form November 03, 2007; Published online November 11, 2007
Abstract
The Euclidean quantum field theory for the fields φ_{Δx}(x), which depend on both the position x and the resolution Δx, constructed
in SIGMA 2 (2006), 046,
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.
Key words:
wavelets; quantum field theory; regularisation.
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