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Magnetic Flux Quantization from Gauge Symmetry

We've shown that we can compute the function
from the vector potential.

A superconductor excludes the magnetic field so we have our field free region.
If we take a ring of superconductor, as shown, we get a condition on the magnetic flux through the center.

Consider two different paths from
to
.

**The difference between the two calculations of f is the flux.**
Now
is not a physical observable so the
does not have to be zero, but,
does have to
be single valued.

**The flux is quantized.**
Magnetic flux is observed to be quantized in a region enclosed by a superconductor.
however, the fundamental charge seen is
.

Jim Branson
2013-04-22