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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

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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

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