Perturbative Approach to Non-renormalizable Theories

TL;DR

This paper presents a novel perturbative method for non-renormalizable theories by introducing finite additional parameters, successfully eliminating infinities and matching exact solutions.

Contribution

It introduces a perturbative approach for non-renormalizable theories using finite expansion parameters to remove infinities, supported by specific quantum mechanics and quantum field theory examples.

Findings

Infinities can be eliminated in non-renormalizable theories using additional parameters.

Perturbative series match exact analytical solutions.

Method applies to delta-function potentials and certain quantum field models.

Abstract

On the perturbatively non-renormalizable and non-perturbatively finite examples (delta-function type potential in non-relativistic quantum mechanics and the mathematical model of the propagator by Redmond and Uretsky in quantum field theory) we illustrate that one can develop a perturbative approach for non-renormalizable theory. The key idea is the introduction of finite number of additional expansion parameters which allows us to eliminate all infinities from the perturbative expressions. The generated perturbative series reproduce the expansions of the exact analytical solutions.