PHS3131 - Theoretical physics - 2018

This unit consists of three 12-lecture sub-units. The three sub-units cover the following areas:

1. Relativistic Dynamics: tensors in pseudo-Euclidean spaces, Lorentz transforms, world lines, energy-momentum 4-vectors, action and variational methods, Lagrangians and Hamiltonians, consequences of Einstein's assumptions.
2. Electrodynamics: Magnetic induction: Ohm's law, electromotive force, time dependent Maxwell's equations. Electric and magnetic fields in matter: polarisation, bound charges, magnetisation, bound currents, linear materials. Maxwell's equations and electromagnetic energy in matter. Boundary conditions and conservation theorems. Electromagnetic waves: monochromatic plane waves in linear media; energy and momentum. Reflection and transmission of electromagnetic waves. Guided waves.
3. Classical Dynamics: 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.

On completion of this unit students will be able to:

1. Recall fundamental concepts from the sub-unit of electrodynamics, which include time dependent Maxwell's equations, energy-momentum conservation and the Poynting vector, the Maxwell stress tensor, electromagnetic waves in vacuum and matter: polarisation, reflection and transmission, guided waves, and resonant cavities.
2. Recall fundamental concepts from the sub-unit of Special Relativity, which include The ultimate speed, Einstein's box and the inertia of energy, energy, momentum and mass, the nature of light, the Michelson-Morley experiment, inertial reference frames, Einstein's two axioms for special relativity, events, the Lorentz transformations and properties, relativity of simultaneity, Newtonian limit and the Galilean transformations, difference and differential versions of the Lorentz transformations, Lorentz invariance of squared interval, relativistic speed limit and causality, group properties of the Lorentz transformation, the drag effect, the relativistic Doppler effect, Hubble's Law and quasars, aberration and visual appearance of moving objects, spacetime and four-tensors, world-lines and light cones, manipulation of four-tensors, four-velocity and four-acceleration, introduction to relativistic particle mechanics, conservation of four-momentum, relativistic billiards, the centre-of-momentum frame, threshold energies, three-force and four-force, Scalar and vector potentials for classical electromagnetic fields, Lorentz covariance of classical electrodynamics, Lorentz transformation of electromagnetic fields, and the Euler-Lagrange field equations.
3. Recall fundamental concepts from the sub-unit of Classical Dynamics, which include Newton's laws of motion, The principle of least action, changing coordinate systems, constraints and generalised coordinates, Noether's theorem and symmetries, the dynamics of classical fields, space-time and internal symmetries, the gauge principle, quantisation of fields, and the vacuum.
4. Solve new problems in physics related to the core concepts of the unit by drawing on the theoretical underpinnings that illustrate the physics.

Examinations (3 hours plus 2 hours): 70%

Assignments: 30%

• Three 1-hour lectures and two 1-hour tutorials per week
• Seven hours of independent study per week

See also Unit timetable information

Astrophysics

Physics