Kirchhoff diffraction optics and the nascent Aharonov–Bohm effect: a theorem

Abstract

Textbook diffraction optics, Kirchhoff diffraction, is connected to the Aharonov–Bohm effect of quantum mechanics by an easy theorem proved here. The connection is between the Kirchhoff wave field and the Aharonov–Bohm quantum wave field in the limit of zero flux: the ‘nascent’ Aharonov–Bohm effect. The diffracting opaque screen of Kirchhoff optics is replaced in the quantum mechanics by a magnetic flux line, or loop, in the shape of the boundary edge of the screen. The gauge must be chosen appropriately: a delta function on that surface, spanning the boundary edge, which matches the screen.