Teaching

Below are some of the courses that I have taught including notes, solutions and useful information for current students.

Part II

Principles of Quantum Mechanics

Quantum mechanics underlies the whole of modern physics and indeed day-to-day life. Without it, Hydrogen atoms would be unstable, fridge-magnets wouldn't exist and the lasers inside every CD and DVD player would be but a dream. Indeed, the whole of life on earth only exists because there is a quantum resonance in Carbon-12.

The course begins by introducing the ideas of operators and state vectors in quantum mechanics as well as some of the physical principles such as energy measurements and the quantum harmonic oscillator. We then move beyond exact solutions an turn our attention to systems that cannot be solved exactly. These systems are tackled using time-independent perturbation theory. We next turn our attention to rotations and angular momentum in quantum mechanics and look at how to add them together. Finally, we look at particle decays and time-dependent perturbations, both of which lie at the heart of quantum mechanics in the real world and govern everything from the opacity of stars to the production and decay rates of new particles at the LHC.

Problem Sets:

Supervision 1:	Set 1	Additional Problems 1
Supervision 2:	Set 2	No additional problems
Supervision 3:	Set 3	No additional problems
Supervision 4:	Set 4	Additional Problems 4

Cosmology

Cosmology is the study of the origin and evolution of the universe. In 1823 Heinrich Wilhelm Olbers came across an apparent paradox: if the universe is static and eternal then why is the sky at night dark when it should be infinitely bright with stars? The solution to this is found in the observation that the universe is accelerating at that not all of the light has reached us yet, and some never shall. As Edgar Allen Poe put it in 1848:

"Were the succession of stars endless, then the background of the sky would present us a uniform luminosity, like that displayed by the Galaxy – since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all."

Cosmology is a wonderful area of study which brings together concepts and ideas from all over physics including general relativity, particle physics, statistical physics, stellar structure theory, quantum mechanics, optics and quantum field theory. Ultimately, the fate of the universe depends on what's in it and so there are hardly any areas of fundamental physics which do not affect the evolution of the universe.

The course begins by studying the expanding universe, both in terms of its evolution and how one can measure distances and angles. We then move on to look at the evolution of particles in an expanding universe and describe the statistical properties of both the photons and the baryons. Next, we change track a bit and study the structure and evolution of main-sequence, white dwarf and neutrons stars. After that we turn our attention to the origin of the light elements and photons in Big Bang Nucleosynthesis and recombination before going on to study the formation of structure in the universe and the cosmic microwave background.

Problem Sets:

Supervision 1:	Set 1
Supervision 2:	Set 2
Supervision 3:	Set 3
Supervision 4:	Set 4

Statistical Physics

Statistical physics is the study of the properties of many body systems. Given that the standard order of magnitude for the number of particles in an average-sized container is 10²³ we can hardly keep track of the position and velocity of each individual particle, however we can describe the global properties of the entire system in terms of a few simple macroscopic thermodynamic variables such as temperature, entropy and free energy. This allows us to fully predict how a specific system will behave when these properties are altered and how it will interact with others. Statistical physics has many applications in modern physics, from condensed matter physics describing the behaviour of solids to the properties of cold stars such as white dwarfs and even the fluctuations of light moving through the universe.

The course begins by introducing the partition function, which is an elegant way of calculating the macrophysical properties of a system given the fundamental interactions between its individual particles. We then use this to calculate the properties of some simple classical and quantum systems before going on to look at some interesting effects in quantum gasses such as Bose-Einstein condensation and zero-temperature Fermi gasses. Finally, we turn to classical thermodynamics and the theory of phase transitions.

Problem Sets:

Supervision 1:	Set 1	Additional Problems 1
Supervision 2:	Set 2	No additional problems
Supervision 3:	Set 3	No additional problems
Supervision 4:	Set 4	Additional Problems 4

David Tong's lecture notes are particularly useful for this course.

Part III

Quantum Field Theory

Field theories are an extremely useful way to describe systems with a larger number of degrees of freedom. By quantising the perturbations of classical fields we can describe the excitation and interactions of one or more particles within a consistent framework. Quantum field theory is the language which describes the whole of particle physics and can be used to calculate the interaction and decay rates for the fundamental particles we have observed in all our experiments, including the LHC. The standard model of particle physics includes quantum field theory. It is also the theory which describes physics on very short length scales and at very high energies and so any fundamental theory should include it one way or another. Beyond particle interactions, quantum field theory can be used to describe other phenomena in condensed matter physics and inflation in the early universe. The course begins by introducing classical field theories and examining how symmetry properties can lead to conserved currents and charges via Noether's theorem. After examining the free Klein-Gordon and Maxwell fields, canonical quantisation is introduced and used to quantise these theories in the Heisenberg and Schrödinger pictures. We then turn our attention to the Lorentz group and its representations and use the spinor representation to describe spin-1/2 particles in terms of Dirac spinor fields, which we then quantise. Leaving free fields behind, we move on to look at interacting quantum field theories and derive a perturbative solution for the time-evolution operator in the interaction picture, which we then use to calculate S-matrix elements for the scattering and decays of different fields. Finally, we turn our attention to quantum electrodynamics, the theory of light interacting with matter and derive the Feynmann rules for this theory.

Problem Sets:

Class 1:	Set 1
Class 2:	Set 2
Class 3:	Set 3
Class 4:	Set 4

David Tong's lecture notes are particularly useful for this course, however, you should be aware that his notes cover the material in a different order to the lectures and the problem sets.

Supersymmetry

The Coleman-Mandula theorem states that the only quantum field theories with a non-trivial S-matrix are those whose underlying symmetry group is the direct product of a group which containts a Poincare sub-group and a lie group whose generators commute with the Poincare generators. Supersymmetry can evade this theorem because its generators are spinorial and has received a lot of attention in recent years for its appealing properties such as powerful non-renormalisation theorems and miraculous cancellations. String theory requires supersymmetry to remove the tachyon mode and supersymmetric extensions of the standard model are of interest because they can alleviate the hierarchy problem. Inflation requires a symmetry in order to keep the inflaton mass small and drive the expansion and supersymmetry is one viable candidate.

The course begins by introducing spinor and the supersymmetry algebra and deriving its Casimir operators. These are then used to construct irreducible representations of the super-Poincare group, which we use to extract the number of particles, and their properties, in each representation. We then formulate supersymmetry in superspace and look for superfields transforming under these irreducible representations. Using this, we calculate the symmetry transformations of the field and use them to construct supersymmetric Lagrangians. Finally, we look at the properties of these Lagrangians, both in terms of supersymmetry breaking and the MSSM

Problem Sets:

Class 1:	Set 1
Class 2:	Set 2
Class 3:	Set 3

The lecture notes from Fernando Quevedo's course are very close to the current one, however they go into more detail. Beware of changes in the sign conventions. Other useful resources are:

A Supersymmetry Primer

ABC of SUSY

Supersymmetry in Particle Physics

Supersymmetry and the MSSM