Wavelet-Based Quantum Field Theory

TL;DR

This paper develops a wavelet-based Euclidean quantum field theory where fields depend on position and resolution, leading to finite Feynman diagrams and a novel regularization method consistent with known radiative corrections.

Contribution

It introduces a wavelet transform approach to quantum field theory, providing a new regularization scheme that ensures finiteness of Feynman diagrams without traditional divergences.

Findings

Feynman diagrams become finite with the wavelet-based regularization.

The method aligns with existing calculations of radiative corrections.

Transition to standard theory achieved via integration over scales.

Abstract

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.