Multi-scale methods in quantum field theory

TL;DR

This paper explores the use of Daubechies wavelets for multi-scale decomposition of quantum fields, enabling finite-dimensional modeling of reactions within finite volumes, and discusses flow equation methods for constructing effective theories.

Contribution

It introduces a wavelet-based multi-scale approach to quantum field theory and applies flow equations to decouple scales, providing a new framework for finite-volume quantum reactions.

Findings

Wavelet decomposition allows exact multi-scale analysis of quantum fields.

Finite energy reactions in finite volumes have a finite number of relevant degrees of freedom.

Flow equations effectively decouple coarse and fine scale degrees of freedom.

Abstract

Daubechies wavelets are used to make an exact multi-scale decomposition of quantum fields. For reactions that involve a finite energy that take place in a finite volume, the number of relevant quantum mechanical degrees of freedom is finite. The wavelet decomposition has natural resolution and volume truncations that can be used to isolate the relevant degrees of freedom. The application of flow equation methods to construct effective theories that decouple coarse and fine scale degrees of freedom is examined.