Renormalization in Wavelet basis

TL;DR

This paper explores how wavelet-based methods can be used for non-perturbative renormalization in quantum field theories, demonstrating a flow of coupling constants through a model with key relativistic features.

Contribution

It introduces a non-perturbative wavelet-based framework for regularization and renormalization in quantum field theories, with practical demonstration on a two-dimensional Dirac delta potential model.

Findings

Successful non-perturbative regularization and renormalization using wavelet basis

Emergence of flowing coupling constants in the model

Model exhibits features typical of relativistic quantum field theories

Abstract

Discrete wavelet-based methods promise to emerge as an excellent framework for the non-perturbative analysis of quantum field theories. In this work, we investigate aspects of renormalization in theories analyzed using wavelet-based methods. We demonstrate the non-perturbative approach of regularization, renormalization, and the emergence of flowing coupling constant within the context of these methods. This is tested on a model of the particle in an attractive Dirac delta function potential in two spatial dimensions, which is known to demonstrate quintessential features found in a typical relativistic quantum field theory.