A Path (Integral) to Scale Invariance

TL;DR

This paper introduces a path integral approach to construct scale invariant quantum field theories by modifying the integration measure, enabling exact scale invariance and addressing anomalies both perturbatively and non-perturbatively.

Contribution

It presents a novel path integral formulation that ensures exact scale invariance in quantum field theories, extending beyond perturbation theory to include non-perturbative effects.

Findings

Reproduces scale invariant regularization in perturbation theory

Provides a framework for non-perturbative scale invariance

Allows construction of quantum theories from classically invariant actions

Abstract

We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having an extra determinant under the integral. In perturbation theory, this extra determinant reproduces the bottom-up procedure of scale invariant regularization, providing an order-by-order cancellation of the scale anomaly together with new non-renormalizable vertices. Our formulation here, however, goes beyond perturbation theory and it is also suitable to study non-perturbative effects. It allows to formulate a scale invariant quantum theory out of any classically invariant action.