## November 8, 2006

### Quantization and Cohomology (Week 4)

#### Posted by John Baez

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 $\omega = dp_i \wedge dq^i$ on the cotangent bundle gives $\omega(v_H, -) = dH$, 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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