This module provides an introduction to the modern theory of gravitation based on Einstein's general theory of relativity. Topics to be covered include: basic elements of geometry, special relativity, equivalence principle, general relativity and curved spacetime, Schwarzschild solution, solar system tests of general relativity, and Schwarzschild black hole.
This module will develop the ideas behind General Relativity (GR) to an advanced level. GR is based on the geometry of four dimensional space-time, the curvature of which is governed by the Einstein’s equations. Some solutions to these equations will be presented, including black holes and cosmological solutions. Gravity in the weak field limit will be derived from the full theory, demonstrating how you should understand the gravitational interaction in terms of graviton exchange. The module will then move on to advanced topics. This includes modified gravity models (eg models with extra dimensions) that are at the forefront of current research.
This module starts off with an introduction to Friedmann models and hot big bang, followed by a review of thermal history, freezeout, relics, recombination, last scattering, and dark matter candidates. Further topics include structure formation, gravitational lensing and its use in detecting dark matter, CMB anisotropies and the lambda CDM model, inflation theory and fluctuations from inflation, and dark energy.
The modern study of general relativity requires familiarity with a number of tools of differential geometry, including manifolds, symmetries, Lie Groups, differentiation and integration on manifolds. These are introduced using examples of curved space-times.
General relativity predicts the existence of black holes which are regions of space-time into which objects can be sent but from which no classical objects can escape. This module uses techniques learned in Differential Geometry to systematically study black holes and their properties, including horizons and singularities. Astrophysical processes involving black holes are discussed, and there is a brief introduction to black hole radiation discovered by Hawking.
Gravity, Particles and Fields Dissertation
This is the substantial investigation that you will carry out on a topic related to the taught modules of the course. The study will be largely self-directed, with oversight and input provided by a supervisor from the School of Mathematical Sciences or the School of Physics and Astronomy. The topic will be chosen from a list of potential projects provided by the school. The topic could be based on a theoretical investigation, a review of research literature, or a combination of the two.
Quantum Field Theory
Quantum Field Theory is the study of the quantum dynamics of relativistic particles. This module gives the quantum description of the electrons, photons and other elementary particles, including a discussion of spin, and bosons and fermions. Lectures will provide an introduction to functional integrals, Feynman diagrams, and the standard model of particle physics.
Introduction to Quantum Information Service
This module gives an introduction to Quantum Information Theory and its applications. We start by introducing the mathematical formalism of quantum theory, including notions of linear operators and tensor products, followed by the operational framework involving the fundamental concepts of states, measurements, and entanglement. In the second part we discuss the basic but influential results in the field such as quantum teleportation, Bell's theorem, and quantum cryptography. This is followed by an introduction to quantum computation and quantum algorithms, the analysis of the structure of noisy quantum channels, and basic notions of quantum error correction theory.
The above is a sample of the typical modules that we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Due to the passage of time between commencement of the course and subsequent years of the course, modules may change due to developments in the curriculum and information is provided for indicative purposes only.