Summation and renormalization of bubble graphs to all orders

TL;DR

This paper presents a novel 2PPI expansion method that sums bubble graphs to all orders and can be renormalized with standard counterterms, applied specifically to the O(N) linear sigma model.

Contribution

The paper introduces the 2PPI expansion for summing bubble graphs to all orders and demonstrates its renormalizability within a mass independent scheme.

Findings

The 2PPI expansion effectively sums bubble graphs to all orders.

The expansion can be renormalized with standard counterterms.

Application to the O(N) linear sigma model shows practical utility.

Abstract

We introduce the 2PPI expansion which sums the bubble graphs to all orders. We show that this expansion can be renormalised with the usual counterterms in a mass independent scheme. We discuss its application to the O(N) linear sigma model.