Unitarity of the Aharonov-Bohm Scattering Amplitudes

TL;DR

This paper examines the unitarity of Aharonov-Bohm scattering amplitudes, revealing that different treatments satisfy unitarity under various regularization schemes, highlighting unresolved theoretical foundations.

Contribution

It analyzes the unitarity relations of Aharonov-Bohm scattering amplitudes across different approaches, clarifying their consistency and underlying assumptions.

Findings

Original amplitude satisfies unitarity with an unclear theoretical basis

Ruijsenaars' amplitude also satisfies unitarity in an unusual manner

Different incident wave treatments lead to distinct unitarity behaviors

Abstract

We discuss the unitarity relation of the Aharonov-Bohm scattering amplitude with the hope that it distinguishes between the differing treatments which employ different incident waves. We find that the original Aharonov-Bohm scattering amplitude satisfies the unitarity relation under the regularization prescription whose theoretical foundation does not appear to be understood. On the other hand, the amplitude obtained by Ruijsenaars who uses plane wave as incident wave also satisfies the unitarity relation but in an unusual way.