I have found a beatiful post by Terry Tao, a Fields medallist, about gauge theories. See here for a worthwhile reading. This post is truly elucidating and so well written that I thought it was worthing a larger audience.
This entry was posted on Monday, September 29th, 2008 at 4:54 pm and is filed under mathematics, Physics. You can follow any responses to this entry through the RSS 2.0 feed.
You can leave a response, or trackback from your own site.
I had read the first few paragraphs of that Terry Tao post and had concluded I wasn’t going to learn anything from it. On your suggestion I’ve looked again, and yes, it is a beautiful post. I like the terms “spent” and “bought”. However, his examples of broken gauge symmetries don’t seem similar to what a physicist thinks of. He seems to see them as methods in proving a result for a symmetry which a physicist would call unbroken.
I’m busily writing up a paper on the CKM and MNS mixing matrices. Terry’s article makes it clear that one can think of the choice of unitary matrix, that produces a given set of experimental data (i.e. the absolute magnitudes), is a form of gauge freedom. When we choose a particular parameterization we are spending that freedom.
And the example of the winds on the earth as defining a direction on each point of the earth, except for the hairy billiard ball theorem, reminds me of an analogous fact about spinors, one that is “one brick in the wall” in why I like density matrices over state vectors as far as quantum mechanics goes.
Suppose for each spin -1/2 spinor, you make a choice of the arbitrary complex phase. For example, you might choose the top component (i.e. the spin up component of the spinor) as real. Then it is a fact that your choice of complex phase cannot be continuous. In this the pure density matrices are more natural.
And before you ask I should add that the paper I’m writing will be sent in for the painful process of peer review. I still don’t have any great attraction to the process, but my co-author needs to “publish or perish”.
Fill in your details below or click an icon to log in:
You are commenting using your WordPress.com account. ( Log Out / Change )
You are commenting using your Twitter account. ( Log Out / Change )
You are commenting using your Facebook account. ( Log Out / Change )
You are commenting using your Google+ account. ( Log Out / Change )
Connecting to %s
Notify me of new comments via email.
RSS - Posts
RSS - Comments
Now on Facebook!
Create a free website or blog at WordPress.com.
Get every new post delivered to your Inbox.
Join 76 other followers