Interaction with External Electromagnetic Field

This lecture covers the interaction with an external electromagnetic field, focusing on classical physics concepts such as proper time, electric charge, and gauge transformations. The instructor discusses the impact of the electromagnetic field on particles and the Hamiltonian, emphasizing the importance of conjugate momenta and kinetic momentum. The lecture also delves into quantum physics, exploring the matrix elements of the kinetic momentum and probability density. Additionally, the concept of gauge invariance and the prob. current are addressed, providing a comprehensive overview of the topic.