On the predictivity of the non-renormalizable quantum field theories

TL;DR

This paper extends the concept of predictivity to non-renormalizable quantum field theories using a Four Dimensional Renormalization approach, enabling systematic quantum corrections with minimal measurements.

Contribution

It introduces topological renormalization, allowing finite parameter values and eliminating the need for traditional ultraviolet infinity absorption in non-renormalizable theories.

Findings

Finite parameter values achieved without traditional renormalization.

One additional measurement suffices for quantum corrections at any loop order.

Ultraviolet divergences are managed without absorbing infinities into the Lagrangian.

Abstract

Following a Four Dimensional Renormalization approach to ultraviolet divergences (FDR), we extend the concept of predictivity to non-renormalizable quantum field theories at arbitrarily large perturbative orders. The idea of topological renormalization is introduced, which keeps a finite value for the parameters of the theory by trading the usual order-by-order renormalization procedure for an order-by-order redefinition of the perturbative vacuum. One additional measurement is then sufficient to systematically compute quantum corrections at any loop order, with no need of absorbing ultraviolet infinities in the Lagrangian.