Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 105, 13 pages      arXiv:0711.1671      https://doi.org/10.3842/SIGMA.2007.105
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Wavelet-Based 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 φΔx(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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