The majorant method for the fermionic effective action

TL;DR

This paper refines the majorant method for controlling fermionic effective actions by addressing a gap in the original formulation and demonstrates its application to a fermion model with local quartic interaction.

Contribution

It identifies and fixes a gap in the original majorant method for fermionic effective actions and applies the improved method to a specific fermion model.

Findings

Confirmed the existence of the majorant equation under new conditions

Validated the method on a fermion model with quartic interaction

Established the analogy with the original formulation by Brydges and Wright

Abstract

We revisit the problem of controlling Polchinski's equation by the solution of an associate Hamilton-Jacobi equation which determines a norm majorant for the fermionic effective action. This method, referred to as the majorant method, was first introduced by D. Brydges and J. Wright in 1988, but its original formulation contains a gap which has never been addressed. We overcome this gap and show that the majorant equation and its existence condition are analogous to the ones originally obtained by Brydges and Wright. As an application of the method, we investigate a fermion model with a local quartic interaction.