The mass gap and vacuum energy of the Gross-Neveu model via the 2PPI expansion

TL;DR

This paper introduces the 2PPI expansion method, proves its renormalizability, and applies it to the Gross-Neveu model to compute the mass gap and vacuum energy, yielding qualitatively accurate results.

Contribution

The paper presents a novel 2PPI expansion technique, demonstrating its renormalizability and effectiveness in calculating key physical quantities in the Gross-Neveu model.

Findings

Successful calculation of the mass gap and vacuum energy

Qualitatively good results after optimization

Validation of the 2PPI expansion as a summation method

Abstract

We introduce the 2PPI (2-point-particle-irreducible) expansion, which sums bubble graphs to all orders. We prove the renormalizibility of this summation. We use it on the Gross-Neveu model to calculate the mass gap and vacuum energy. After an optimization of the expansion, the final results are qualitatively good.