Infinite reduction of couplings in non-renormalizable quantum field theory

TL;DR

This paper explores a method to systematically reduce and classify the infinite couplings in non-renormalizable quantum field theories, potentially enabling high-order predictions by relating irrelevant terms to a finite set of parameters.

Contribution

It introduces an infinite reduction approach based on perturbative meromorphy and analyticity, providing a framework to handle irrelevant interactions in non-renormalizable theories.

Findings

Reduction can be based on perturbative meromorphy or analyticity.

Number of couplings remains finite or grows slowly with order.

Framework helps classify and select physical irrelevant interactions.

Abstract

I study the problem of renormalizing a non-renormalizable theory with a reduced, eventually finite, set of independent couplings. The idea is to look for special relations that express the coefficients of the irrelevant terms as unique functions of a reduced set of independent couplings lambda, such that the divergences are removed by means of field redefinitions plus renormalization constants for the lambda's. I consider non-renormalizable theories whose renormalizable subsector R is interacting and does not contain relevant parameters. The "infinite" reduction is determined by i) perturbative meromorphy around the free-field limit of R, or ii) analyticity around the interacting fixed point of R. In general, prescriptions i) and ii) mutually exclude each other. When the reduction is formulated using i), the number of independent couplings remains finite or slowly grows together with the order of the expansion. The growth is slow in the sense that a reasonably small set of parameters is sufficient to make predictions up to very high orders. Instead, in case ii) the number of couplings generically remains finite. The infinite reduction is a tool to classify the irrelevant interactions and address the problem of their physical selection.