The role of electron orbital angular momentum in the Aharonov–Bohm effect revisited

Abstract

This is a brief review on the theoretical interpretation of the Aharonov-Bohm effect, which also contains our new insight into the problem. A particular emphasis is put on the unique role of electron orbital angular momentum, especially viewed from the novel concept of the physical component of the gauge field, which has been extensively discussed in the context of the nucleon spin decomposition problem as well as the photon angular momentum decomposition problem. Practically, we concentrate on the frequently discussed idealized setting of the Aharonov-Bohm effect, i.e. the interference phenomenon of the electron beam passing around the infinitely-long solenoid. One of the most puzzling observations in this Aharonov-Bohm solenoid effect is that the pure-gauge potential outside the solenoid appears to carry non-zero orbital angular momentum. Through the process of tracing its dynamical origin, we try to answer several fundamental questions of the Aharonov-Bohm effect, which includes the question about the reality of the electromagnetic potential, the gauge-invariance issue, and the non-locality interpretation, etc.

Can classical electrodynamics predict nonlocal effects?

“…Let us now apply (19) to this charge-solenoid configuration where the volume V covers all space except the volume of the solenoid. Here we have L P = 0 because B = 0 outside the solenoid and therefore (19) We also note that a different and less general two-dimensional decomposition of the Poynting formula L P was introduced by Wakamatsu et al [4] (this decomposition contains a sign mistake), which involves a two-dimensional Coulomb field produced by the moving electron whose velocity is assumed to be "much slower than the speed of light," a condition that, according to the authors, allows them to discard the magnetic field of the moving electron. They obtained the relation L M = −L S and interpreted the piece −L S as an electromagnetic angular momentum originated by the return flux.…”

“…Using the Poynting formula 3 x for an electromagnetic angular momentum in a volume V , we come directly to the conclusion that the electromagnetic angular momentum of the charge-solenoid configuration vanishes outside the solenoid because the magnetic field is zero in this region. However, Wakamatsu et al [4] recently used the Maxwell formula [7]: 3 x for an electromagnetic angular momentum and arrived at the conclusion that the electromagnetic angular momentum of the charge-solenoid configuration is given by L = qΦẑ/(2πc) outside the solenoid. This same result was previously obtained by Tiwari [3] using a Lagrangian treatment.…”

“…The interesting point is that in these same free-field regions, quantum mechanics predicted the existence of the AB phase δ = eΦ/(hc). However, the comments of Tassie and Peshkin received little attention and the idea that (1) could shed light on the interpretation of the AB effect did not seem to have been explored further until in recent years in which Tiwari [3] and Wakamatsu et al [4] derived (1) and drew attention to the role that plays (1) in the context of the AB a e-mail: ricardo.heras.13@ucl.ac.uk (corresponding author) 0123456789(). : V,-vol effect.…”

“…We then show that (1) is the electromagnetic angular momentum of this configuration. In contrast to Tiwari [3] and Wakamatsu et al [4], who discuss (1) in connection to the AB effect, we only consider this connection when we suggest that (1) may be interpreted as the classical counterpart of the AB phase. Our main purpose here is to argue that (1) describes a nonlocal interaction between the charge moving outside the solenoid and the magnetic flux inside this solenoid, which answers in the affirmative the question posed in the title of this paper.…”

A still unsettled issue in the nucleon spin decomposition problem: On the role of surface terms and gluon topology

“…For an interacting system of photons and charged particles, however, the longitudinal part of J γ also gives nonzero contributions. With use of partial integration supplemented with the Gauss law ∇ ′ · E (x ′ ) = ρ(x ′ ), the longitudinal part J γ can be transformed into the following form [44] :…”