Comparison of mass renormalization schemes for simple model systems

TL;DR

This paper introduces an alternative mass renormalization method for quantum field Hamiltonians that ensures no self-scattering in vacuum and single-particle sectors, comparing it with standard spectral techniques and exploring non-perturbative approaches.

Contribution

It presents a novel renormalization scheme based on sector stability and discusses its application to simple bosonic models, offering a potential non-perturbative computational method.

Findings

The new method successfully renormalizes quadratic and quartic bosonic interactions.

Results are consistent with standard spectral analysis for simple models.

Potential for non-perturbative quantum field theory renormalization is discussed.

Abstract

We discuss an alternative method to mass renormalize a quantum field Hamiltonian based on a requirement that the vacuum and single-particle sectors are not self-scattering. We illustrate the feasibility of this method for the concrete example of bosonic quadratic and also quartic interactions. The results are compared with those obtained by the standard renormalization technique based on a spectral analysis of the usual field-based propagators. We also discuss a potential method for renormalizing a quantum field theory in a non-perturbative way using computational methods.