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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 ω=dp idq i\omega = dp_i \wedge dq^i on the cotangent bundle gives ω(v H,)=dH\omega(v_H, -) = dH, where the Hamiltonian vector field v Hv_H is given by v H=Hp iq iHq ip iv_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)
Weblog: The n-Category Café
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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