Sometimes, quantities have singularities because of a bad choice of coordinates. For example, if you measure wind velocity in terms of degrees of latitude and longitude per second, you're going to have a problem at the north pole, but if you choose different coordinates, the problem goes away. Other times, quantities might have "real" singularities, and no coordinate choice can fix them.
A choice of gauge is basically the big brother of choosing coordinates, in a much more general setting. Roughly speaking, I'm trying to figure out how to tell when a certain kind of object (a Yang-Mills connection) has a singularity due to a bad choice of gauge, and then I want to pick a better gauge to make the singularity go away.
Read other answers by Yasha Berchenko-Kogan on Quora:
- What are the most important mathematics papers or other written works in each century?
- Do you find it easier to write your own proof than to read and comprehend someone else's?
- Are there any pure mathematical theorems that can help us to significantly compress strings of huge numbers (billions of digits)?
from Quora http://ift.tt/2bGH99I
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