Charge-flux composite

A charge-flux composite carries electric charge $q$ and localized magnetic flux $\Phi$. Mutual encircling of $(q_1,{\Phi }_1)$ and $(q_2,{\Phi }_2)$ produces the phase $\exp [i(q_1{\Phi }_2+q_2{\Phi }_1)/\hslash ]$ from the Aharonov-Bohm and Aharonov-Casher effects.

The Aharonov-Bohm effect is the phase $q\Phi /\hslash$ acquired when a charge $q$ encircles magnetic flux $\Phi$, even when the magnetic field vanishes along the charge's path.

The Aharonov-Casher effect is the electromagnetic dual in which a magnetic moment or flux acquires a phase by encircling electric charge.