School of Physics and Astronomy MSci Module Index

Description: This module provides a first introduction into the unification of last century's groundshaking revolutions in physics: Special Relativity and Quantum Mechanics. Relativistic wave equations for particles of various spins are derived and studied, and the physical interpretations of their solutions are analyzed. Students will learn about the fundamental concepts of quantum field theory, starting with classical field theory, quantisation of the free Klein-Gordon and Dirac field and the derivation of the Feynman propagator. Then interactions are introduced and a systematic procedure to calculate scattering amplitudes using Feynman diagrams is derived. Finally, the quantisation of the electro-magnetic field is discussed and the relativistic cross sections for various physically relevant examples are calculated.

Description: This module offers an explanation of the fundamental principles of General Relativity. This involves the analysis of particles in a given gravitational field and the propagation of electromagnetic waves in a gravitational field. The derivation of Einstein's field equations from basic principles is included. The derivation of the Schwarzchild solution and the analysis of the Kerr solution inform discussion of physical aspects of strong gravitational fields around black holes. The generation, propagation and detection of gravitational waves is mathematically analysed and a discussion of weak general relativistic effects in the Solar System and binary pulsars is included as a discussion of the experimental tests of General Relativity.

Description: Research in astrophysics builds on a vast body of literature and archived data. This module is an introduction to research methods which exploit existing information sources in astrophysics. The module serves as preparation for the research project which forms a major part of the MSc programme. In this module students will learn how to review and evaluate with critical insight, the current state of research of a chosen area in astrophysics. They will receive training in writing academic reports in an appropriate style, and will learn how to convey research material in a presentation. Additional topics will be included so that students are prepared for project work at an advanced level. These can include specific exercises in using astronomical data archives, scientific word processing, mathematical skills, using mathematical and data analysis packages, project planning, etc.

Description: As the planetary system most familiar to us, the Solar System presents the best opportunity to study questions about the origin of life and how enormous complexity arise from simple physical systems in general. This module surveys the physical and dynamical properties of the Solar System. It focuses on the formation, evolution, structure, and interaction of the Sun, planets, satellites, rings, asteroids, and comets. The module applies basic physical and mathematical principles needed for the study, such as fluid dynamics, electrodynamics, orbital dynamics, solid mechanics, and elementary differential equations. However, prior knowledge in these topics is not needed, as they will be introduced as required. The module will also include discussions of very recent, exciting developments in the formation of planetary and satellite systems and extrasolar planets (planetary migration, giant impacts, and exoplanetary atmospheres).

Description: Stars are important constituents of the universe. This module starts from well known physical phenomena such as gravity, mass conservation, pressure balance, radiative transfer of energy and energy generation from the conversion of hydrogen to helium. From these, it deduces stellar properties that can be observed (that is, luminosity and effective temperature or their equivalents such as magnitude and colour) and compares the theoretical with the actual. In general good agreement is obtained but with a few discrepancies so that for a few classes of stars, other physical effects such as convection, gravitational energy generation and degeneracy pressure have to be included. This allows an understanding of pre-main sequence and dwarf stages of evolution of stars, as well as the helium flash and supernova stages.

Description: The module will introduce Feynman's path integral formulation of Quantum Mechanics and apply it to study of Quantum Field Theory (QFT). Emphasis will be given to the role of symmetries (Ward identities), the renormalisation group and the idea of effective action. The concept of Wilson's effective action and the different nature of (ir)relevant/marginal terms will be discussed. Simple scalar theories will provide the example where to apply the concepts and the techniques introduced. The course will also touch on some more advanced topics, such as quantum anomalies and conformal field theories.

Description: The aim of this course is to complement the core Relativistic Waves and Quantum Fields (RWQF) module by providing the student with some advanced tools essential for research in modern Theoretical Physics. Using the same starting point as RWQF, Maxwell's theory of electromagnetism, we will focus on the Lagrangian formulation of the two most prominent theories of our time: Yang-Mills (gauge) theory and gravity. The alternative notation of differential forms will be explored and the geometric aspects of gauge theory emphasised. Building on this, and introducing elements from group theory and fibre bundles we will introduce classical solitons as localised, finite energy solutions to the classical field equations in various dimensions (kinks in 2d, vortices in 3d, monopoles in 4d, instantons in Euclidean 4d) and discuss their properties, including the existence of zero-modes, associated collective coordinates and moduli spaces.

Description: This module gives a broad exposition of the modern frame work for the unification of special relativity and quantum theory -- relativistic quantum field theory (QFT). Lagrangian formulation and canonical quantisation of free fields with spin = 0, 1/2, 1 are revised. The construction of interacting quantum field theories is devoloped with special focus on phi^4-theory and quantum electrodynamics (QED). Perturbation theory in terms of Feynman diagrams is developed systematically, and important concepts such as regularisation and renormalisation are introduced. These tools are applied to the calculation of simple tree-level and one-loop S-matrix elements and cross-sections in phi^4 theory and QED, corrections to the electron magnetic moment and the running coupling. The course will also touch on more advanced topics such as anomalies, non-Abelian gauge theories, and modern methods for the calculation of S-matrix elements.

Description: A plasma is an ionized gas where the magnetic and electric field play a key role in binding the material together. Plasmas are present in almost every astrophysical environment, from the surface of pulsars to the Earth's ionosphere. This module explores the unique properties of plasmas, such as particle gyration and magnetic reconnection. The emphasis is on the plasmas found in the Solar System, from the solar corona and solar wind to the outer reaches of the heliosphere and the interstellar medium. Fundamental astrophysical processes are explored, such as the formation of supersonic winds, magnetic energy release, shock waves and particle acceleration. The module highlights the links between the plasmas we can observe with spacecraft and the plasmas in more distant and extreme astrophysical objects.

Description: This module is an introduction to understanding the origin, propagation, detection and interpretation of electromagnetic (EM) radiation from astronomical objects. In this module students will learn: how to describe EM radiation and its propagation through a medium to an observer; the main processes responsible for line and continuum emission and how they depend on the nature and state the emitting material; the effects of the earth's atmosphere and the operation of the detection process at various wavelengths. The material will be illustrated by examples from optical, infrared and radio portions of the EM spectrum.

Description: Electronic structure methods - that is, computational algorithms to solve the Schrodinger equation - play a very important role in physics, chemistry and materials science. These methods are increasingly treated on a equal footing with experiment in a number of areas of research, a sign of their growing predictive power and increasing ease of use. This course will cover the fundamental theoretical ideas behind these methods. Topics will include Hartree-Fock, correlated methods like Moller-Plesset perturbation theory, configuration interaction, coupled-cluster as well as density-functional theory. The theoretical ideas will be complemented with a hands-on computational laboratory using state-of-the-art programs with the aim of providing our students with a basic understanding of the technical implementations and strengths and shortcomings of these methods.

Description: Ever since the dawn of civilization human beings have speculated about the existence of planets outside of the Solar System orbiting other stars. The first bona fide extrasolar planet orbiting an ordinary main sequence star was discovered in 1995, and subsequent planet searches have uncovered the existence of more than one hundred planetary systems in the Solar neighbourhood of our galaxy. These discoveries have reignited speculation and scientific study concerning the possibility of life existing outside of the Solar System. This module provides an in depth description of our current knowledge and understanding of these extrasolar planets. Their statistical and physical properties are described and contrasted with the planets in our Solar System. Our understanding of how planetary systems form in the discs of gas and dust observed to exist around young stars will be explored, and current scientific ideas about the origin of life will be discussed. Rotationally supported discs of gas (and dust) are not only important for explaining the formation of planetary systems, but also play an important role in a large number of astrophysical phenomena such as Cataclysmic Variables, X-ray binary systems, and active galactic nuclei. These so-called accretion discs provide the engine for some of the most energetic phenomena in the universe. The second half of this module will describe the observational evidence for accretion discs and current theories for accretion disc evolution.

Description: The module considers in detail the basic physical processes that operate in galaxies, using our own Galaxy as a detailed example. This includes the dynamics and interactions of stars, and how their motions can be described mathematically. The interstellar medium is described and models are used to represent how the abundances of chemical elements have changed during the lifetime of the Galaxy. Dark matter can be studied using rotation curves of galaxies, and through the way that gravitational lensing by dark matter affects light. The various topics are then put together to provide an understanding of how the galaxies formed.

Description: This module covers advanced concepts of modern cosmology, and in particular will introduce the student to cosmological perturbation theory. It discusses the observed structure of the universe, how these structures formed, and how they can be used to test our theories and models of the universe. The module will also discuss recent and upcoming experiments and large scale structure surveys and their relevance for cosmology.

Description: This course introduces core concepts in supersymmetry that can be applied to quantitatively understand a broad variety of physical systems and is a complement to the AQFT and FMQFT modules. Starting with supersymmetric quantum mechanics as a toy model, the course covers the supersymmetry algebra, its representations, the Witten Index, and the resulting constraints on quantum dynamics. We then move on to introduce supersymmetric field theories in three space-time dimensions consisting of scalars and fermions while giving a basic introduction to symmetry currents, the classical and quantum Wilsonian renormalization group flow, moduli spaces, spurions, and non-renormalization arguments. The course culminates in a study of simple dualities in three-dimensional supersymmetric abelian gauge theories. We conclude with a discussion of supersymmetry in four space-time dimensions and, time permitting, the embedding of our constructions in string theory.

Description: The module will cover the basics of string theory including the classical relativistic physics of the string, its quantisation and the resulting spectrum. This will then be extended to examine so called p-branes and the basics of M-theory.

Description: Machine learning influences modern life through many different avenues and is silently revolutionising the way we live and work. We can see the influence of machine learning algorithms in social media, web search engines, mobile device spell checkers and self-driving cars. This module provides an introduction to machine learning using the Python programming language and the TensorFlow (TM) programming toolkit from Google (TM). Minimal programming background is assumed, however students wishing to take this module should be familiar with using computers, and mathematics at a level commensurate with a BSc in Physics or equivalent degree (calculus and linear algebra).

Description: This module is an introduction to the use of computational methods in astrophysics. The material presented in this module consists of the following: Basic notions of computer algorithms: Introduction to numerical analysis: approximations, errors, convergence, stability, etc; Finite difference methods: solution of ordinary and partial differential equations; Introduction to numerical methods used in data analysis: image processing, spectral analysis, etc. Students will also be introduced to the a range of astrophysical data and related online resources. The concepts will be illustrated with authentic examples from astrophysics, such as solar system dynamics, astrophysical fluids, stellar structure, etc. Computer practical courseworks using Python are a major element of the module. Students will write simple programs, and present their results in written reports. The module is intended to cater for students with very different levels of programming expertise.

Description: The MSc research Project is at the heart of the MSc programme. It is an independent project undertaken by the student within a working research group in the School. The project runs over three semesters in order to allow for the student to both design their project (using available literature etc.), be trained in the relevant techniques and carry out a reasonably substantial piece of research based on an actual (real) research problem. The presentation of the student findings is based both on a formal, technical written report (75 page maximum length) and on an oral presentation (e.g. powerpoint talk) and examination.

Description: PA student will develop design, experimental, computational or analytical skills through the independent study of a problem in physics. S/he will learn to write a scientific report summarising results of an independent investigation and placing them in a physics context. The project will run through both semesters and will involve keeping a research log (see 'Engagement Log' elsewhere on this page), interim coursework, a final written report and oral assessment at the end of semester B.
The aim of the investigative project is to give the student the opportunity to work independently on a chosen project towards specified goals. These goals will vary from project to project and may include: writing software to achieve a specified computational task, e.g., simulation of a physical process; carrying out a series of measurements to establish or disprove a working hypothesis; building a piece of equipment, e.g., to interface an experiment to a PC; analytical mathematical analysis applied to the study of a theoretical problem.

Description: You will develop design, experimental, computational or analytical skills through the independent study of a problem in physics. You will learn to write scientific reports summarising results of an independent investigation and placing them in a physics context, and detailing the methods used and the results obtained. The project will run through both semesters and will involve an interim report at the end of semester 1 as well as the final reports at the end of semester 2.

Description: The MSc project involves a critical review of a chosen topic in modern astrophysics, and may include some original research. Students write a dissertation summarising current research in that chosen field and the extent of their own investigations.