I was reading an article about the Aharonov - Bohm effect and gauge invariance ( J. Phys. A: Math. Gen. 16 (1983) 2173-2177 ) and there is something I really don't get it.(adsbygoogle = window.adsbygoogle || []).push({});

The facts are:

The problem is the familiar Aharonov-Bohm one, in which we have a cylinder and inside the cylinder [tex]\rho < R[/tex] there is a magnetic field [tex]\vec{B} = B \hat{e}_z[/tex].

The writers wanted to use a different gauge (than the usual written in books) which is, in cylindrical coordinates [tex](\rho, \phi, z)[/tex],

[tex]A_{\rho} = - \rho B_z \phi[/tex]

At this gauge the vector potential [tex]\vec{A}[/tex] vanishes when [tex]\vec{B}[/tex] does, i.e. when [tex]\rho > R[/tex].

Furthermore the vector potential is a multivalued function.

The writer in order to "fix" this problem cuts the space and considers the space as a union of two regions:

[tex]0 < \phi < 2 \pi[/tex] and [tex]-\pi < \phi < \pi[/tex]

He defines in these regions two different potentials

[tex]A_{\rho}^1 = - \rho B_z \phi ,\ \ \ 0 < \phi < 2\pi[/tex], and

[tex]A_{\rho}^2 = - \rho B_z \phi' ,\ \ \ -\pi < \phi' < \pi[/tex].

Ok here is my question...

How can I calculate the correct Flux for a curve [tex]C[/tex] for [tex]\rho > R[/tex] ?

i.e. [tex]\Phi = \int \vev{A} \cdot dl[/tex] which must be [tex]\Phi = \pi R^2 B_z[/tex].

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Aharonov Bohm Effect (gauge invariance)

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**