Theories with Finite Green's Functions

TL;DR

This paper explores how adding specific nonrenormalizable terms to free scalar field theories can produce Green's functions that are less singular or finite, enabling the extraction of physical insights via lattice methods.

Contribution

It demonstrates that certain nonrenormalizable modifications yield Green's functions with improved singularity properties, including finiteness, which can be studied using lattice techniques.

Findings

Green's functions become less singular or finite with added nonrenormalizable terms

Lattice methods can extract physical information from these theories

Potential for new approaches to nonrenormalizable quantum field theories

Abstract

The addition of certain nonrenormalizable terms to the usual action density of a free scalar field leads to nonrenormalizable theories whose exact euclidian and minkowskian Green's functions are less singular than those of the free theory. In some cases, they are finite. One may use lattice methods to extract physical information from these less-singular, nonrenormalizable theories.