Canonical Transformations in Hamiltonian Formalism

This lecture covers canonical transformations in the Hamiltonian formalism, focusing on the rules to make such transformations and their significance in the context of the harmonic oscillator. The instructor explains the concept of canonical transformations, the Hamiltonian equations, and the preservation of the action principle. The lecture emphasizes the gauge invariance and the structure necessary for these transformations. Various examples and comparisons are provided to illustrate the key points, leading to a deeper understanding of the topic.