Pion-Nucleon Scattering in Kadyshevsky Formalism: II Baryon Exchange Sector

TL;DR

This paper develops Lorentz-invariant, causal baryon exchange amplitudes for pion-nucleon scattering within the Kadyshevsky formalism, incorporating pair suppression and analyzing frame dependence, with results linked to phase shifts.

Contribution

It introduces a formalism for constructing baryon exchange amplitudes in pion-nucleon scattering that ensures Lorentz invariance and causality, extending previous work with new methods.

Findings

Amplitudes are Lorentz invariant and causal.

Frame dependence of the integral equation is analyzed.

Phase shifts are connected to invariant amplitudes.

Abstract

In this paper, which is the second part in a series of two, we construct tree level baryon exchange and resonance amplitudes for $\pi N$ / $MB$-scattering in the framework of the Kadyshevsky formalism. We use this formalism to formally implement absolute pair suppression, where we make use of the method of Takahashi and Umezawa. The resulting amplitudes are Lorentz invariant and causal. We continue studying the frame dependence of the Kadyshevsky integral equation using the method of Gross and Jackiw. The invariant amplitudes, including those for meson exchange, are linked to the phase-shifts using the partial wave basis.