Classical Mechanics

Teaching assistant material of Harvard Physics 151: Mechanics (Fall 2024, Arthur Jaffe). It provides a mathematical perspective on the boundary between classical and quantum mechanics, with applications ranging from symmetry principles to field theory.

Prof Jaffe’s Mechanics course, which has been taught for decades, features a mathematical introduction to classical mechanics with emphasis on the symmetry-conservation duality as well as intuition for quantum constructions. The main deliverables are:

1. Covariant versus action-extremization perspectives on Lagrangian mechanics.
2. Convex duality between Lagrangian and Hamiltonian mechanics; the Legendre transform.
3. Symmetry-conservation symmetry using Noether’s theorem and Hamiltonian flow (symplectic gradient).
4. Representation of the Lorentz group.
5. Field mechanics and local conservation.

This course was my first introduction to differential geometry and Lie theory. My final project on Koopman von-Neumann theory (Fall ‘23) inspired my later interests in:

1. Exploring the boundary between classical and quantum theory.
2. Quantum phase space, later combined with interest in information theory.
3. The adjoint problem: characterizing possible dynamics of a composite system by observing its components.