One-particle irreducibility of Vilkovisky-DeWitt effective action

TL;DR

This paper verifies that the Vilkovisky-DeWitt effective action can be expressed as a sum of one-particle irreducible diagrams up to three-loop order, confirming a fundamental property of the formalism.

Contribution

It provides a detailed verification of the one-particle irreducibility property of VDEA up to three loops in non-gauge theories, extending previous understanding.

Findings

Confirmed one-particle irreducibility of VDEA up to three loops

Validated the formalism's consistency in non-gauge theories

Enhanced understanding of the structure of the Vilkovisky-DeWitt effective action

Abstract

The effective action formalism introduced by Vilkovisky and later modified by DeWitt is completely covariant suitable for obtaining an effective action that is independent of the parametrization of the quantum fields. Among a few basic properties of an effective action, one property is that it can be written as a sum of one-particle irreducible diagrams. In this work, we verify this property up to three-loop order for Vilkovisky-Dewitt effective action (VDEA) by solving the equations satisfied by VDEA written down in the original parametrization for non-gauge theories.