M7 · Canonical transformations
A 20-module path through m7 · canonical transformations, in study order from foundations to the frontier.
Modules
- Definition of Canonical Transformations
- Generating Functions and the Four Types
- Type-1 Generating Function F1(q,Q,t)
- Type-2 Generating Function F2(q,P,t)
- Type-3 and Type-4 Generating Functions
- Symplectic Condition
- Symplectic Group and Phase-Space Geometry
- Poisson Brackets: Definition
- Algebra of Poisson Brackets
- Fundamental Poisson Brackets
- Poisson Brackets as a Test for Canonicity
- Poisson-Bracket Formulation of Dynamics
- Constants of Motion via Poisson Brackets
- Infinitesimal Canonical Transformations
- Generators of Continuous Transformations
- Hamiltonian as Generator of Time Evolution
- Momentum and Angular Momentum as Generators
- Symmetries and Conservation Laws in Hamiltonian Form
- Liouville's Theorem and Phase-Space Volume
- Canonical Invariants and Poincaré Integral Invariants