Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

December 21, 2006

Quantization and Cohomology (Week 9)

Posted by John Baez

Here are the final notes from my Fall 2006 course on Quantization and Cohomology:

  • Week 9 (Dec. 5) - A glimpse of what’s to come. Phases versus relative phases. Geometric quantization: finding a connection on a U(1) bundle whose curvature is the symplectic 2-form ω on phase space. Why doing this is only possible if ω defines an integral cohomology class - hence the term ‘quantization’.

Last week’s notes are here; the notes from next quarter begin here.

My colleague Apoorva Khare has produced a LaTeX version of the notes for the entire Fall quarter, and Christine Dantas has drawn figures for these notes. The notes still need more polishing, but they’re already very useful:

Posted at December 21, 2006 2:51 AM UTC

TrackBack URL for this Entry:   http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/1082

7 Comments & 3 Trackbacks

Read the post Quantization and Cohomology (Week 8)
Weblog: The n-Category Café
Excerpt: From particles to membranes, continued.
Tracked: December 21, 2006 3:37 AM

Re: Quantization and Cohomology (Week 9)

Adding figures to the document sounds like a fun thing to do over Christmas break!

Posted by: Blake Stacey on December 21, 2006 4:52 PM | Permalink | Reply to this

Re: Quantization and Cohomology (Week 9)

That’s the right attitude! And, if a bunch of folks want to split the work, we can arrange that. For more, see this.

Posted by: John Baez on December 21, 2006 7:29 PM | Permalink | Reply to this
Read the post A Little Bit of Geometric Langlands: Relation to Integrable Systems
Weblog: The n-Category Café
Excerpt: On Hitchin integrable systems and their role in geometric Langlands duality.
Tracked: December 21, 2006 5:50 PM

Re: Quantization and Cohomology (Week 9)

Christine Dantas has offered to try creating figures for these lecture notes. We’ll see how it goes.

Posted by: John Baez on December 22, 2006 2:37 AM | Permalink | Reply to this

Re: Quantization and Cohomology (Week 9)

Christine prepared figures over the Christmas break! Hurrah for Christine!

I still need to check the figures and maybe edit them a bit. Then they need to be incorporated into the text.

Posted by: John Baez on January 2, 2007 8:34 PM | Permalink | Reply to this

Re: Quantization and Cohomology (Week 9)

Thanks!

And it was great to learn some drawing tips from you.

After you review the figures (and if there are some you want me to improve), I can incorporate their final version in the LaTeX file of the Lecture Notes, if you like.

Best wishes,
Christine

Posted by: Christine Dantas on January 3, 2007 11:37 PM | Permalink | Reply to this

Re: Quantization and Cohomology (Week 9)

Christine wrote:

I can incorporate their final version in the LaTeX file of the Lecture Notes, if you like.

Oh, that would be excellent! Thanks!

They look generally quite good at a first glance, but I’ll have to carefully check them for various little problems…

I don’t know why Apoorva Khare included slots for pictures that weren’t in Derek’s notes. As far as I know, Derek copies all the pictures that I draw on the board — and both of us are pretty careful to draw all the pictures needed to explain an idea (and no more). So, perhaps in most cases we should adjust Apoorva’s notes to match Derek’s pictures. I’ll have to check.

Posted by: John Baez on January 3, 2007 11:57 PM | Permalink | Reply to this

Re: Quantization and Cohomology (Week 9)

I’m certain we will soon converge to a reasonable final version of these figures! I’ll be waiting for your check on the (few) missing pictures and other necessary corrections and then I’ll incorporate them.

Perhaps I’ll have a few questions on the course contents as well, but I have not finished studying all material yet…

Thanks
Christine

Posted by: Christine Dantas on January 4, 2007 12:25 AM | Permalink | Reply to this
Read the post Quantization and Cohomology (Week 10)
Weblog: The n-Category Café
Excerpt: Classical versus quantum mechanics: the Lagrangian and Hamiltonian approaches
Tracked: January 17, 2007 1:07 AM

Post a New Comment