Classical dynamics and field theory

This unit examines topics in Classical dynamics and Classical field theory. The important mathematical framework, and the approach to describing physical systems developed in these fields of study, are applicable to much of modern physics, and provide an essential foundational basis for further studies in physics. The unit consists of two theory-only subunits, and the key areas of study are:

• Classical dynamics: Elements of tensor calculus, the principle of extremal action, coordinate transformations, constraints and generalised coordinates. Noether's theorem, space-time and gauge symmetries. The Hamiltonian formalism, Liouville's theorem, Poisson's brackets. Canonical transformations, connection to quantum mechanics. Path integral formulation of quantum physics. Applications for classical point particles and non-relativistic fields.

• Classical field theory: Maxwell's equations, Electromagnetic waves in vacuum and matter, gauge transformations, fields of a moving point charge, dipole radiation, Lorentz transformations, relativistic electrodynamics, tensor notation, the field tensor, electrodynamics in tensor notation.