Microscopic theory of the Aharonov-Bohm effect
Departamento de Física Moderna, Universidad
de Cantabria - 39005-Santander, Spain
2 Departamento de Optica, Facultad de Ciencias Físicas, Universidad Complutense 28040-Madrid, Spain
Accepted: 8 December 1998
A fully quantum theory of the Aharonov-Bohm effect is presented. It is based on the interaction, mediated by virtual photon exchange, between the traveling electron and the atomic magnetic dipoles of an infinitely long permanent magnet. The calculation involves second-order time-dependent perturbation theory. As expected, the relative phase between the two states —corresponding to the two alternative paths— interfering on the screen agrees with that predicted in the usual theory. However our method may allow to get corrections, for instance due to the size and shape of the electron wave packet, the possible soft-photon emission or the excitation of the atoms in the magnet.
PACS: 03.65.Bz – Foundations, theory of measurement, miscellaneous theories (including Aha ro nov-Bohm effect, Bell inequalities, Berry's phase) / 12.20.-m – Quantum electrodynamics
© EDP Sciences, 1999