Quantization and Cohomology (Week 4)

November 8, 2006

Quantization and Cohomology (Week 4)

Posted by John Baez

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Here are the notes for the October 24th class on Quantization and Cohomology:

Week 4 (Oct. 24) - Hamiltonian dynamics and symplectic geometry. Hamiltonian vector fields. Getting Hamiltonian vector fields from a symplectic structure. The canonical 1-form on a cotangent bundle, and how this gives a symplectic structure.
- Homework: show the symplectic structure $ω = {dp}_{i} \land {dq}^{i}$ on the cotangent bundle gives $ω (v_{H}, -) = dH$ , where the Hamiltonian vector field $v_{H}$ is given by $v_{H} = \frac{\partial H}{\partial p_{i}} \frac{\partial}{\partial q^{i}} - \frac{\partial H}{\partial q_{i}} \frac{\partial}{\partial p^{i}}$

Last week’s notes are here; next week’s notes are here.

Posted at November 8, 2006 5:34 AM UTC

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Read the post Quantization and Cohomology (Week 3)
Weblog: The n-Category Café
Excerpt: Sorry for the long pause! Here are the notes for the October 17th class on Quantization and Cohomology: Week 3 (Oct. 17) - From Lagrangian to Hamiltonian dynamics. Momentum as a cotangent vector. The Legendre transform. The Hamiltonian. Hamilton's...
Tracked: November 8, 2006 5:59 AM

Read the post Quantization and Cohomology (Week 5)
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Excerpt: The canonical 1-form on the cotangent bundle of a manifold, and what it does for classical mechanics.
Tracked: November 13, 2006 7:58 AM

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November 8, 2006