The Transition from Quantum Field Theory to One-Particle Quantum Mechanics and a Proposed Interpretation of Aharonov–Bohm Effect

Abstract

In this article we demonstrate a sense in which the one-particle quantum mechanics (OPQM) and the classical electromagnetic four-potential arise from quantum field theory (QFT). In addition, the classical Maxwell equations are derived from a QFT scattering process, while both classical electromagnetic fields and potentials serve as mathematical tools to approximate the interactions among elementary particles described by QFT physics. Furthermore, a plausible interpretation of the Aharonov-Bohm (AB) effect is raised within the QFT framework. We provide a quantum treatment of the source of electromagnetic potentials and argue that the underlying mechanism in the AB effect can be understood via interactions among electrons described by QFT where the interactions are mediated by virtual photons.

Geometric Phases and The Sagnac Effect: Foundational Aspects and Sensing Applications

“…However, there is no final consensus on this issue and, thus, the origins of this phase are investigated until this day with works that include the idea of modular variables [61] and models that consider the source of magnetic field as part of the dynamics or quantize the magnetic field itself. [85,[90][91][92][93][94][95][96][97][98][99][100][101][102] Furthermore, the interplay between Berry and AB phases in various scenarios can also be of interest. For instance, the phases acquired by a quantum charge with a large spreading while it encircles one or multiple solenoids were studied in ref.…”

Geometric phases and the Sagnac effect: Foundational aspects and sensing applications

“…As a result, it is typically considered to be of nonlocal nature. However, there is no final consensus on this issue and, thus, the origins of this phase are investigated until this day with works that include the idea of modular variables [60] and models that consider the source of magnetic field as part of the dynamics or quantize the magnetic field itself [84,[89][90][91][92][93][94][95][96][97][98][99][100][101]. Furthermore, the interplay between Berry and AB phases in various scenarios can also be of interest.…”

Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond

“…Alternatively, the Aharonov-Bohm effect highlights a nonlocal (or global) aspect of quantum mechanics allowing electromagnetic fields to affect the charge even in regions from which they are excluded (1,4,5,6,7,8). Debates regarding fundamental aspects of the Aharonov-Bohm effect remain vivid until this day (9,10,11,12,13,14,15).…”