A New Renormalization Group for Hamiltonian Field Theory

TL;DR

This paper introduces a novel renormalization group approach for Hamiltonian field theory, demonstrating how effective field theory and similarity renormalization techniques can manage divergences and errors in quantum systems like the two-dimensional delta-function potential.

Contribution

It presents a new renormalization group method tailored for Hamiltonian field theories, combining effective field theory and similarity renormalization techniques.

Findings

Control of logarithmic errors achieved

Control of inverse-power-law errors demonstrated

Application to delta-function potential illustrates effectiveness

Abstract

The Schrodinger equation with a two-dimensional delta-function potential is a simple example of an asymptotically free theory that undergoes dimensional transmutation. Renormalization requires the introduction of a mass scale, which can be lowered perturbatively until an infrared cutoff produced by non-perturbative effects such as bound state formation is encountered. We outline the effective field theory and similarity renormalization group techniques for producing renormalized cutoff hamiltonians, and illustrate the control of logarithmic and inverse-power-law errors both techniques provide.