Some nonrenormalizable theories are finite

TL;DR

This paper identifies specific nonrenormalizable theories that are finite in their Green's functions and action densities, challenging the notion that nonrenormalizable theories are inherently singular or non-physical.

Contribution

It demonstrates the existence of four nonrenormalizable theories with finite Green's functions and action densities, expanding the understanding of nonrenormalizable quantum field theories.

Findings

Four nonrenormalizable theories have finite Euclidean and Minkowskian Green's functions.

Two theories possess finite Euclidean action densities and describe scalar bosons with finite mass.

The space of nonsingular nonrenormalizable theories is extensive.

Abstract

Some nonrenormalizable theories are less singular than all renormalizable theories, and one can use lattice simulations to extract physical information from them. This paper discusses four nonrenormalizable theories that have finite euclidian and minkowskian Green's functions. Two of them have finite euclidian action densities and describe scalar bosons of finite mass. The space of nonsingular nonrenormalizable theories is vast.