Classical Field Theory

Classical Field Theory is a theoretical framework that describes how physical fields, like electromagnetic fields or gravitational fields, interact with matter and energy. In Lagrangian and Hamiltonian mechanics, we analyze systems by focusing on their energy and motion over space and time. Lagrangian mechanics emphasizes the difference between kinetic and potential energy, while Hamiltonian mechanics reformulates this in terms of coordinates and momenta. Together, they provide powerful tools to derive the equations governing the dynamics of fields and particles, offering insights into phenomena like wave propagation and the behavior of forces in nature.