Wavelets in Field Theory

TL;DR

This paper proposes using Daubechies wavelets as a basis in quantum field theory, offering natural cutoffs and a connection to renormalization group fixed points, to improve the analysis of field problems.

Contribution

It introduces Daubechies wavelets as a basis for quantum field theory, highlighting their advantages like cutoffs and relation to renormalization group fixed points.

Findings

Wavelet basis provides natural large volume and short distance cutoffs.

Wavelet functions relate to the fixed point of a linear renormalization group.

The approach facilitates partitioning of unity in field theory analysis.

Abstract

We advocate the use of Daubechies wavelets as a basis for treating a variety of problems in quantum field theory. This basis has both natural large volume and short distance cutoffs, has natural partitions of unity, and the basis functions are all related to the fixed point of a linear renormalization group equation.