Math 249     Mechanics     Fall 2006

• Monday, September 25
• Wednesday, September 27
• Monday and Wednesday, October 2 and 4
• Derivation of Euler-Lagrange equations on Lie groups
• Canonical symplectic structure, October 16 and 18 (first part)
• Symplectic manifolds, October 23 (Exercises are as described in class, not in notes -- I recycled some old notes.)
• Hamilton's equations and Poisson brackets, October 25 (plus some proofs)
• Poisson brackets, October 30
• Quantization, and quantization on manifolds (November 6, 8, some of 13)
• Quantization of the rigid body, part 1 (November 22, some of 27)

Homework

• First homework assignment (target due date: October 16)

Optional supplemental readings
(really optional—some of this will involve analytic or topological results, or applications, that I definitely don't assume you all know or want to know)

• Definitions and results for Lie groups, from Foundations of Mechanics, Abraham and Marsden. The relevant material is indicated with a vertical line in the left margin; the topological results, particularly those pertaining to quotients, are far beyond what we'll need. I'll define in class, homework, etc, any of this that we need.