Magnetic flux and its topological effects in Aharonov-Bohm effect

TL;DR

This paper explains the Aharonov-Bohm effect by showing how confined magnetic flux alters the topology of the charge's configuration space, leading to observable phase shifts without direct magnetic interaction.

Contribution

It provides a topological explanation for the nonlocal phase shift in the Aharonov-Bohm effect, emphasizing the role of configuration space puncture.

Findings

Magnetic flux causes a topological change in the configuration space.

The phase shift arises from the altered topology, not direct magnetic interaction.

The work clarifies the nonlocality in the Aharonov-Bohm effect.

Abstract

The Aharonov-Bohm effect is a physical phenomenon in which the quantum state of a charged particle acquires a phase shift that is directly proportional to the magnetic flux, $\Phi$, due to a (classical) magnetic field, ${\mathbf B}$, which is confined in a spatial region from which the magnetic field cannot escape. Even though the charged particle is not allowed to interact with the magnetic field, it accumulates a phase shift that affects the interference pattern produced. Not surprisingly, this apparent nonlocality is puzzling and counter intuitive. In this work, we provide an explanation that explains the physics underlying this apparent nonlocality. We find that the role of the confined magnetic field is to impart a puncture in the configuration space, $\mathbb{R}^2$, of the charge. Therefore, the quantum state corresponding to the charged quantum particle acquires the phase shift due to its response to the modified topology of the configuration space, $\mathbb{R}^2-\{0\}$, corresponding to the charge.