Wavelets and renormalization group in quantum field theory problems

TL;DR

This paper introduces a wavelet-based regularization method for scale-dependent quantum field theories, complementing the functional renormalization group approach by summing larger scale fluctuations to derive effective actions.

Contribution

It develops a wavelet transform-based regularization technique for quantum field theories, providing an alternative to traditional renormalization group methods.

Findings

Reproduces standard RG results for the $^4$ model.

Analyzes fixed points in one-loop approximation.

Demonstrates the method's effectiveness in scale-dependent models.

Abstract

Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the fluctuations of larger scales in order to get the effective action at small observation scale (M.V.Altaisky, Phys. Rev. D93(2016) 105043. The standard RG results for $\phi^4$ model are reproduced. The fixed points of the scale-dependent theory are studied in one loop approximation.