Gravity, Particles and Fields MSc

The fundamental laws of physics have a profound geometric character. This fact can only be appreciated by familiarising oneself with modern differential geometry, to which this module gives an introduction. The topics covered include manifolds, in particular geometric objects that can be placed on manifolds, such as vector fields, differential forms and more generally tensors. The module also discusses symmetries, including the notion of infinitesimal symmetries as captured by Killing vector fields. Integration of differential forms, including the Stokes’ theorem is covered as well. The final part of the module gives an introduction to Lie Groups and Lie algebras, building up to the description of Lie algebras in terms of left-invariant vector fields on the group manifold.  

This module provides an introduction to the modern theory of gravitation: Einstein's general theory of relativity.

Topics to be covered include:

• Specifying geometry
• Special relativity
• Equivalence principle
• General relativity
• Schwarzschild solution
• Schwarzschild black hole

This module will develop the ideas behind general relativity (GR) to an advanced level. You will explore solutions to these equations including black holes and cosmological solutions.

You will also have the opportunity to study more advanced topics including modified gravity models (eg models with extra dimensions) that are at the forefront of current research.

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 develops techniques 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. 

This module facilitates an understanding of Friedmann models and hot big bang. It encompasses the study of thermal history, freezout, relics, recombination, last scattering; dark matter candidates.

Other topics will include inflation, fluctuations from inflation, structure formation, gravitational lensing CMB anisotropies, and dark energy.

This module provides an introduction to the theoretical and conceptual foundations of quantum field theory, which is a highly versatile and important subject in modern theoretical and mathematical physics. After a short review of some elementary aspects of classical field theory, the first part of this module introduces the crucial concept of field quantisation and develops perturbative methods leading to the famous Feynman diagrams. The more advanced component of this module includes the study of renormalisation techniques for quantum field theories and a discussion of physical applications to quantum electrodynamics and the standard model of particle physics. 

The paradigm of quantum information science is that quantum systems such as atoms and photons are carriers of a new type of information featuring entanglement and coherence properties that are not shared by classical information. The rapidly developing area of quantum technology aims to harness these features in practical applications ranging from new modes of computation to secure communication and precision metrology.

This module provides an introduction to the mathematical theory of quantum information science and its applications. The first part sets out the operational framework involving fundamental concepts of states, measurements, and entanglement and then reviews some of the influential results in the field such as quantum teleportation, Bell's Theorem, and quantum key distribution. The second part introduces the circuit model of quantum computation and discusses simple quantum algorithms. This is followed by the theory of quantum channels and quantum error correction.

The dissertation is an extended piece of research, in an area covered by the taught modules but on a topic linked to a contemporary research forefront. The study will be largely self-directed, with oversight and support provided by a supervisor from the School of Mathematical Sciences or the School of Physics and Astronomy.

The topic could be based on a research investigation, a review of research literature, or a combination of these. You can choose among a range of topics proposed by supervisors or propose an original topic yourself. The dissertation offers an excellent introduction to exciting research topics, insights into how research is conducted, and a solid basis for pursuing a PhD.