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.

November 13, 2006

Quantization and Cohomology (Week 5)

Posted by John Baez

Still catching up… here are the notes for the Halloween class on Quantization and Cohomology:

  • Week 5 (Oct. 31) - The canonical 1-form α\alpha on T *XT^* X. Symplectic structures. Why a symplectic structure should be a nondegenerate 2-form (so we get time evolution from a Hamiltonian) and closed (so time evolution preserves this 2-form). The action expressed in terms of the canonical 1-form.
    • Homework: show that if α\alpha is the canonical 1-form on the cotangent bundle of a manifold, then ω=dα \omega = -d\alpha is a nondegenerate 2-form.
Last week’s notes are here; next week’s notes are here. Posted at November 13, 2006 7:48 AM UTC

TrackBack URL for this Entry:   http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/1032

0 Comments & 3 Trackbacks

Read the post Quantization and Cohomology (Week 6)
Weblog: The n-Category Café
Excerpt: The canonical 1-form, extended phase space and Rovelli's covariant formulation of classical mechanics.
Tracked: November 13, 2006 8:10 AM
Read the post Quantization and Cohomology (Week 4)
Weblog: The n-Category Café
Excerpt: Hamiltonian dynamics and symplectic geometry.
Tracked: January 31, 2007 2:51 AM
Read the post That Shift in Dimension
Weblog: The n-Category Café
Excerpt: What makes the Kontsevich-Cattaneo-Felder theorem tick? How can it be that an n-dimensional quantum field theory is encoded in an (n+1)-dimensional one?
Tracked: August 25, 2007 2:30 AM

Post a New Comment