### 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