Dyson-Schwinger approach to pion-nucleon scattering using time-ordered perturbation theory

TL;DR

This paper develops a non-relativistic quantum field theoretical approach using Dyson-Schwinger equations within Time-Ordered Perturbation Theory to model pion-nucleon scattering, capturing complex absorption and creation processes.

Contribution

It introduces a method to construct partial wave separable $N$ t matrices incorporating full dressing and renormalization, bridging quantum field theory and quantum mechanics.

Findings

Constructed partial wave separable $N$ t matrices.

Demonstrated features of quantum field theory in a non-relativistic framework.

Provided a pedagogical approach to pion-nucleon scattering modeling.

Abstract

We present a simple description of pion-nucleon ($\pi N$) scattering taking into account the full complexity of pion absorption and creation on the nucleon. To do this we solve Dyson-Schwinger equations within the framework of Time-Ordered Perturbation Theory. This enables us to construct partial wave separable $ \pi N$ t matrices that can be useful in models of nuclear processes involving fully dressed nucleons. At the same time, our approach demonstrates features of Quantum Field Theory, like particle dressing, renormalisation, and the use of Dyson-Schwinger equations, in a non-relativistic context that is maximally close to that of Quantum Mechanics. For this reason, this article may also be of pedagogical interest.