On causality, unitarity and perturbative expansions

TL;DR

This paper introduces a pedagogical method for combining micro-causality and unitarity in scattering amplitudes using conformal mappings and perturbative expansions, demonstrated with a Yukawa interaction.

Contribution

It presents a systematic approach to approximate scattering amplitudes that respects causality and unitarity constraints, applicable to complex force interactions.

Findings

Effective analytic extrapolation of partial-wave amplitudes

Systematic approximation method demonstrated with Yukawa interaction

Handles superpositions of short-range and long-range forces

Abstract

We present a pedagogical case study how to combine micro-causality and unitarity based on a perturbative approach. The method we advocate constructs an analytic extrapolation of partial-wave scattering amplitudes that is constrained by the unitarity condition. Suitably constructed conformal mappings help to arrive at a systematic approximation of the scattering amplitude. The technique is illustrated at hand of a Yukawa interaction. The typical case of a superposition of strong short-range and weak long-range forces is investigated.