On the Preservation of Quasilocality by the Integration-Out Transformation

TL;DR

This paper proves that the integration-out step in the renormalization group preserves the quasilocality of the effective action for scalar fields, ensuring the flow invariance of quasilocality under the Polchinski equation.

Contribution

It provides a general proof that the integration-out process maintains quasilocality in the renormalization group flow, applicable to scalar fields on a torus and beyond.

Findings

Integration-out preserves quasilocality of the effective action.

Flow invariance of quasilocality under the Polchinski equation.

Applicable to scalar fields on a torus and more general settings.

Abstract

We demonstrate that the integration-out step of the renormalization group transformation preserves the quasilocality of the effective action. This is shown in the case of a single, real, scalar field on a torus, but the proof holds more generally. The main result can be thought of as showing the flow invariance of the quasilocal subset under the flow generated by the Polchinski equation.