Resummations in the Bloch-Nordsieck model

TL;DR

This paper compares various resummation techniques in the exactly solvable Bloch-Nordsieck model, highlighting the effectiveness of truncated Schwinger-Dyson equations as an exact solution method and its potential for broader applications.

Contribution

It demonstrates that truncated Schwinger-Dyson equations provide an exact solution in the Bloch-Nordsieck model, offering a new approach for more complex theories.

Findings

2PI resummation reduces infrared sensitivity but remains approximate.

One-loop perturbation theory shows infrared sensitivity at the mass shell.

Truncated Schwinger-Dyson equations yield an exact solution in this model.

Abstract

We studied different levels of resummations of the exactly solvable Bloch-Nordsieck model in order to be able to compare the approximations with an exact result. We studied one-loop perturbation theory, 2PI resummation and Schwinger-Dyson equations truncated in a way to maintain Ward-identities. At all levels we carefully performed renormalization. We found that although the 2PI resummation does not exhibit infrared sensitivity at the mass shell (the one-loop perturbation theory does), but it is still far from the exact solution. The method of truncated Schwinger-Dyson equations, however, is exact in this model, so it provides a new way of solving the Bloch-Nordsieck model. This method can also be generalized to other, more complicated theories.