Renormalizable non-renormalizable theories

TL;DR

This paper introduces a general method for constructing continuum limits of field theories and applies it to specific models, demonstrating their equivalence through large N expansions.

Contribution

It presents a new prescription for continuum limit construction and establishes the equivalence between non-linear and linearized models in three dimensions.

Findings

Successful application of the prescription to O(N) sigma and Gross-Neveu models

Demonstration of equivalence between non-linear and linearized models

Use of large N expansion techniques

Abstract

The general prescription for constructing the continuum limit of a field theory is introduced. We then apply the prescription to construct the O(N) non-linear sigma model and the Gross-Neveu model in three dimensions using the large N expansions. We compare these non-linear models with the linearized models, and show the equivalence.