Appendices

A - Michaelmas Courses

 
Advanced Philosophy of Physics 

Department: Philosophy

Lecturers: Prof Adam Caulton, Prof James Read, Prof Christopher Timpson

Course Weight: 1.5 units/24 lectures (continues in Hilary)

Assessment Method: mini-project or homework completion 

Course Synopsis: This series of classes will cover contemporary topics in the philosophy of physics, with emphasis on: thermal physics (thermodynamics and statistical mechanics), the role of symmetries in physical theories, spacetime (especially the general theory of relativity), and advanced topics in the philosophy of quantum theory (which may include the role of decoherence in solving the measurement problem, the interpretation of probability, and topics in quantum field theory). 
Those MMathPhys and MSc students taking the course in the mini-project or homework mode also receive 8 hours of tutorials (usually as one of a pair) from one of the external lecturers. These tutorials are usually spread throughout the year, with the first 4 in Michaelmas Term. Students are expected to produce an essay of between 2,000-2,500 words for each tutorial. For those taking the course in mini-project mode, two of these tutorials will be given over to discussing drafts of the two 5,000-word essays submitted by each candidate for assessment in week 4 of Trinity Term.

Anyons and Topological Quantum Field Theory

Department: Physics

Lecturer: Prof Steve Simon

Course Weight: 1 unit/ 16 lectures

Assessment Method: written exam in HT week 0 or homework completion 

Course Synopsis: The intersection of topology and quantum mechanics is an enormous and still growing field. It touches upon physics topics ranging from quantum gravity to quantum information to materials physics and condensed matter experiment, as well as being one of the most interesting directions in the mathematical study of topology. This is the backdrop upon which we build. A number experiments from the last few years have finally detected and measured anyons — particles that are neither bosons nor fermions – in condensed matter systems (GaAs quantum wells, graphene) as also as in rudimentary quantum computers (superconducting qubits, trapped ion qubits, rydberg atoms). The presence of anyons tells us that our systems are necessarily nontrivial topological quantum field theories! This makes the topic particularly exciting right now!

For a full lecture syllabus, see here: 2024 Anyons Lecture Syllabus

C3.1 Algebraic Topology

Department: Maths

Lecturer: Prof Andras Juhasz

Course Weight: 1 unit/16 lectures

Assessment Method: written exam in TT

General Prerequisites: A3 Rings and Modules is essential, in particular a solid understanding of groups, rings, fields, modules, homomorphisms of modules, kernels and cokernels, and classification of finitely generated abelian groups.
A5 Topology is essential, in particular a solid understanding of topological spaces, connectedness, compactness, and classification of compact surfaces. B3.5 Topology and Groups is helpful but not necessary, in particular the notion of homotopic maps, homotopy equivalences, and fundamental groups will be recalled during the course. There will be little mention of homotopy theory in this course as the focus will be instead on homology and cohomology. 

Course Synopsis: Homology theory is a subject that pervades much of modern mathematics. Its basic ideas are used in nearly every branch, pure and applied. In this course, the homology groups of topological spaces are studied. These powerful invariants have many attractive applications. For example we will prove that the dimension of a vector space is a topological invariant and the fact that ‘a hairy ball cannot be combed’.

C3.3 Differentiable Manifolds

Department: Maths

Lecturer: Prof Dominic Joyce

Course Weight: 1 unit/16 lectures

Assessment Method: written exam in TT

General Prerequisites: A5: Topology and ASO: Introduction to Manifolds are strongly recommended. (Notions of Hausdorff, open covers, smooth functions on R^n will be used without further explanation.) Useful but not essential: B3.2 Geometry of Surfaces.

Course Synopsis: A manifold is a space such that small pieces of it look like small pieces of Euclidean space. Thus a smooth surface, the topic of the Geometry of Surfaces course, is an example of a (2-dimensional) manifold.
Manifolds are the natural setting for parts of classical applied mathematics such as mechanics, as well as general relativity. They are also central to areas of pure mathematics such as topology and certain aspects of analysis.

In this course we introduce the tools needed to do analysis on manifolds. We prove a very general form of Stokes’ Theorem which includes as special cases the classical theorems of Gauss, Green and Stokes. We also introduce the theory of de Rham cohomology, which is central to many arguments in topology.
 

C3.4 Algebraic Geometry

Lecturer: Prof Damian Rossler

Course Weight: 1 unit/16 lectures

Assessment Method: written exam in TT

General Prerequisites: A3 Rings and Modules and B2.2 Commutative Algebra are essential. Noetherian rings, the Noether normalisation lemma, integrality, the Hilbert Nullstellensatz and dimension theory will play an important role in the course. B3.3 Algebraic Curves is useful but not essential. Projective spaces and homogeneous coordinates will be defined in C3.4, but a working knowledge of them would be useful. There is some overlap of topics, as B3.3 studies the algebraic geometry of one-dimensional varieties. Courses closely related to C3.4 include C2.2 Homological Algebra, C2.7 Category Theory, C3.7 Elliptic Curves, C2.6 Introduction to Schemes; and partly related to: C3.1 Algebraic Topology, C3.3 Differentiable Manifolds, C3.5 Lie Groups.

Course synopsis: Algebraic geometry is the study of algebraic varieties: an algebraic variety is roughly speaking, a locus defined by polynomial equations. One of the advantages of algebraic geometry is that it is purely algebraically defined and applied to any field, including fields of finite characteristic. It is geometry based on algebra rather than calculus, but over the real or complex numbers it provides a rich source of examples and inspiration to other areas of geometry.

C5.5 Perturbation Methods

Department: Maths

Lecturer: Prof Ruth Baker

Course Weight: 1 unit/16 lectures

Assessment Method: written exam in TT

General Prerequisites: Knowledge of core complex analysis and of core differential equations will be assumed, respectively at the level of the complex analysis in the Part A (Second Year) course Metric Spaces and Complex Analysis and the phase plane section in Part A Differential Equations I. The final section on approximation techniques in Part A Differential Equations II is highly recommended reading if it has not already been covered.

Course Synopsis: Perturbation methods underlie numerous applications of physical applied mathematics: including boundary layers in viscous flow, celestial mechanics, optics, shock waves, reaction-diffusion equations, and nonlinear oscillations. The aims of the course are to give a clear and systematic account of modern perturbation theory and to show how it can be applied to differential equations.    

C6.1 Numerical Linear Algebra

Department: Maths

Lecturer: Prof Yuji Nakatsukasa

Course Weight: 1 unit/16 lectures

Assessment Method: written exam in TT

General Prerequisites: Only elementary linear algebra is assumed in this course. The Part A Numerical Analysis course would be helpful, indeed some swift review and extensions of some of the material of that course is included here.

Course Synopsis: Linear Algebra is a central and widely applicable part of mathematics. It is estimated that many (if not most) computers in the world are computing with matrix algorithms at any moment in time whether these be embedded in visualization software in a computer game or calculating prices for some financial option. This course builds on elementary linear algebra and in it we derive, describe and analyse a number of widely used constructive methods (algorithms) for various problems involving matrices.

C7.5 General Relativity I

Department: Maths

Lecturer: Dr Christopher Couzens

Course Weight: 1 unit/16 lectures

Assessment Method: written exam in TT

General Prerequisites:  Special Relativity, Classical Mechanics and Electromagnetism

Course Synopsis: The course is intended as an introduction to general relativity, covering both its observational implications and the new insights that it provides into the nature of spacetime and the structure of the universe. Familiarity with special relativity and electromagnetism as covered in the Part A and Part B courses will be assumed. The lectures will review Newtonian gravity, special relativity (from a geometric point of view), and then move on to cover physics in curved space time and the Einstein equations. These will then be used to give an account of planetary motion, the bending of light, the existence and properties of black holes and elementary cosmology. 

Groups and Representations

Department: Physics

Lecturer: Prof Andre Lukas

Course Weight: 1.5 units/ 24 lectures

Assessment Method: written exam in HT week 0 and homework completion

Course Synopsis: Modern theories of particle physics are based on symmetry principles and use group theoretical tools extensively. Besides the standard Poincar´e/Lorentz invariance of all such theories, one encounters internal (continuous) groups such as SU(3) in QCD, SU(5) and SO(10) in grand unified theories (GUTs), and E6 and E8 in string theory. Discrete groups also play an important role in particle physics model building, for example in the context of models for fermion masses.
The main purpose of this course is to develop the understanding of groups and their representations, including finite groups and Lie groups.Emphasis is placed on a mathematically satisfactory exposition as well as on applications to physics and practical methods needed for ”routine” calculations.

For a list of prerequisites and suggested reading see here: Groups and Reps outline

Kinetic Theory

Department: Physics

Lecturers: Prof Alex Schekochihin, Dr Paul Dellar and Dr Robert Ewart

Course Weight: 1.75 units/28 lectures

Assessment Method: written exam in week 0 HT or homework completion

Course Synopsis: 
Part I (9 lectures). Kinetic theory of gases. Timescales and length scales. Hamiltonian mechanics of N particles. Liouville’s Theorem. Reduced distributions. BBGKY hierarchy. Boltzmann-Grad limit and truncation of BBGKY equation for the 2-particle distribution assuming a short-range potential. Boltzmann's collision operator and its conservation properties. Boltzmann's entropy and the H-theorem. Maxwell-Boltzmann distribution. Linearised collision operator. Model collision operators: the BGK operator, Fokker-Planck operator. Derivation of hydrodynamics via Chapman-Enskog expansion. Viscosity and thermal conductivity.
Part II (10 lectures). Kinetic theory of plasmas and quasiparticles. Kinetic description of a plasma: Debye shielding, micro- vs. macroscopic fields, Vlasov-Maxwell equations. Klimontovich’s version of BBGKY (non-examinable). Plasma frequency. Partition of the dynamics into equilibrium and fluctuations. Linear theory: initial-value problem for the Vlasov-Poisson system, Laplace-tranform solution, the dielectric function, Landau prescription for calculating velocity integrals, Langmuir waves, Landau damping and kinetic instabilities (driven by beams, streams and bumps on tail), Weibel instability (non-examinable), sound waves, their damping, ion-acoustic instability, ion-Langmuir oscillations. Energy conservation. Heating. Entropy and free energy. Ballistic response and phase mixing. Role of collisions. Elements of kinetic stability theory. Quasilinear theory: general scheme. QLT for bump-on-tail instability in 1D. Introduction to quasiparticle kinetics.
Part III (9 lectures). Kinetic theory of self-gravitating systems. Unshielded nature of gravity and implications for self-gravitating systems. Virial theorem, negative specific heat and impossibility of thermal equilibrium. Escape, impact of fluctuations. Mean-field approximation, angle-action variables, self-consistent potential, biorthonormal potential-density pairs. Relaxation driven by fluctuations in mean-field. Long-time response to initial perturbation. Fokker-Planck equation. Computation of the diffusion coefficients in terms of resonant interactions. Application to a tepid disc.

For further details see here: Kinetic Theory course

Quantum Field Theory

Department: Physics

Lecturer: Prof John Wheater

Course weight: 1.5 units/24 lectures

Assessment method: written exam in 0 HT

Course synopsis:

1. Introduction, and Why do we need quantum field theory?
2. Relativistic wave equations
3. Formalism of classical field theory
4. Canonical quantisation of the real scalar field
5. Charge and complex fields
6. Canonical quantisation of the fermion field
7. Interacting fields, formalism and the perturbation expansion
8. Scattering and decay, their relation to amplitudes
9. Calculation of low order Feynman diagrams
10. Regularization and renormalizable QFTs

Quantum Matter 1: Phases of Matter and Field Theories

Department: Physics

Lecturer: Prof Steve Simon

Course weight: 1 unit/16 lectures

Assessment method: written exam in week 6-8 TT

Course synopsis: This course serves as part of the C6 theory option and also serves as a notional prerequisite for several of the quantum matter courses
(QM2,QM3,QM4) that follow.

Part 1: Phases and Phase Transitions.  Phase transitions and
Universality.  Landau Theory and Applications.  Ginzburg-Landau
theory: Upper and Lower critical dimensions.  Spontaneous Symmetry
Breaking.  Goldstone modes.  Mermin Wagner Theorem.

Part 2: Many Body Quantum Field Theory.  Working with Fock Space and
Second Quantization.  Applications to Fermi Systems, Weakly interating
Bosons (Bogoliubov theory) and Spin waves.

Quantum Processes in Hot Plasma

Department: Physics

Lecturer: Prof Peter Norreys

Course weight: 0.75 units/12 lectures

Assessment method: homework completion only

Prerequisites: For MMathPhys students, B3 Quantum Atomic and Molecular Physics. For MSc students, basic atomic physic. The lectures in weeks 1 - 2 of the course reviews the principles of atomic physics from first principles, presented in the B3 course. This is to ensure that students who enrol via the MSc route (external to the University) are brought up to date with those enrolling internally via the Oxford undergraduate physics course.

Course synopsis: Hot plasma is ubiquitous throughout the Universe and first appeared in the epoch of recombination that produced the cosmic background radiation about 378,000 years after the Big Bang. Since then quantum processes, particularly the emission and absorption of electromagnetic radiation from plasma, have provided essential information about the macroscopic structure of matter in the visible Universe. They are key to understanding stellar structure and evolution (along with helioseismology) by providing constraints on radiative transfer associated with nucleosynthesis of chemical elements in stellar interiors and in supernovae explosions. The effort to harness the immense power of nuclear fusion using magnetic or inertial confinement fusion schemes is being actively pursued world-wide. Indeed, these plasmas are among the most intense sources of X-rays in the laboratory and are used to study materials under extreme conditions of density and temperature. Emerging new tools, such as X-ray free electron lasers, are also being applied to these problems for the first time.
This course will introduce the student to the use of quantum mechanics in the computational modelling of hot plasmas. In the first part, an introduction to atomic processes is first provided to remind students of the basic principles of Slater’s configurational model and Racah’s tensor operator method. Then, the properties of electronic configurations and transition arrays are described, along with how they are used to replace the corresponding sets of individual levels and radiative lines. Following that, we will describe how these are applied to plasma dynamics and atomic processes, along with elegant new methods of super-configurations and effective temperatures. Finally, current applications are described, along with numerical and experimental examples.