Duality-invariant topological quantum phase of a moving dyon

Abstract

We derive the duality-invariant quantum phase that accumulates a dyon upon encircling a solenoid enclosing electric and magnetic fluxes. The phase is topological because it depends on the number of windings the dyon carries out around the solenoid and is independent of the shape of the dyon trajectory. The phase is nonlocal because there is no generalised Lorentz force locally acting on the dyon and then the electric and magnetic fluxes have no local consequences at any point of the dyon trajectory. We also obtain the energy levels of the proposed dyon-solenoid configuration and envision a quantum two-slit interference experiment associated to the new phase. We show that the duality symmetry of the new phase unifies the Aharonov-Bohm phase with its corresponding dual phase, the Dowling-Williams-Franson phase. This duality symmetry also suggests two new alternative interpretations of the Aharonov-Bohm phase.

Topology, nonlocality and duality in classical electrodynamics

“…This symmetry also allows us to give different physical interpretations for these electromagnetic angular momenta. We have argued that L qg should be considered as the classical counterpart of the duality-invariant quantum phase introduced in 8 . We have also demonstrated, by means of an explicit calculation, that the radiative effects of the Liénard-Wiechert fields of the non-relativistic dyon moving in uniform circular motion around the dual solenoid do not affect L qg .…”

“…This duality symmetry is not only interesting from mathematical point of view but is also interesting from a physical point of view since it allows us to give two different physical interpretations for both L q and L g . We then claim that the z-component of (3) can be considered as the classical counterpart of the duality-invariant quantum phase introduced in 8 : δ D = (qΦ m − gΦ e )/(hc), being both quantities connected by the linear relation δ D = 2πL qg /h. We emphasize the topological nature of L qg by noting that it is independent from the dynamics of the dyon and stress this independence by demonstrating that L qg insensitive to the radiative effects of the Liénard-Wiechert fields of the encircling dyon.…”