On the Preservation of Quasilocality by the Integration-Out Transformation

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.