The quantum phase of a dyon

TL;DR

This paper derives a duality-invariant quantum phase for dyons encircling solenoids, unifying the Aharonov-Bohm phase with its dual, and explores its physical consequences including energy levels and interference effects.

Contribution

It introduces a duality-invariant quantum phase for dyons, unifying known phases and analyzing its physical implications, including energy spectra and scattering.

Findings

Derived the duality-invariant dyon phase.

Connected the phase to energy levels and interference shifts.

Showed spin 1/2 does not alter the phase.

Abstract

When a dyon encircles an infinitely-long solenoid enclosing uniform electric and magnetic fields, its wave function accumulates a duality-invariant quantum phase, which is topological because it depends on a winding number and is nonlocal because the enclosed fields act on the dyon in regions where these fields vanish. Here, we derive this dyon phase and show how its duality symmetry unifies the Aharonov-Bohm phase with its dual phase. We obtain the energy levels, the two-slit interference shift, and the scattering amplitude associated with the duality-invariant quantum phase. Assuming that the dyon has spin 1/2, we show that this spin does not affect the introduced phase. We argue that a spin 1/2 dyon has electric and magnetic moments, the former being greater than the latter because of the Schwinger-Zwanziger quantisation condition.