Validating the 2PI resummation: the Bloch-Nordsieck example

TL;DR

This paper introduces a numerical method to compute the Bloch-Nordsieck spectral function at finite temperature within the 2PI approximation, demonstrating good agreement with exact results after coupling constant matching.

Contribution

It provides a novel numerical approach for finite temperature spectral functions in the 2PI framework and explores the finite temperature running of the coupling constant.

Findings

2PI results match exact spectral functions after coupling matching

Finite temperature running of the 2PI coupling constant is characterized

Method applicable to finite temperature QED coupling behavior

Abstract

In this work we provide a numerical method to obtain the Bloch-Nordsieck spectral function at finite temperature in the framework of the 2PI approximation. We find that the 2PI results nicely agree with the exact one, provided we perform a coupling constant matching. In the paper we present the resulting finite temperature running of the 2PI coupling constant. This result may apply for the finite temperature behavior of the coupling constant in QED, too.