# MSc Modules

#### Advanced Quantum Field Theory

This module gives a broad exposition of the modern framework for the unification of special relativity and quantum theory - relativistic quantum field theory. We will introduce Lagrangian formulation and canonical quantisation of free fields with spin = 0, ½ and 1. We’ll go on to develop the construction of interacting quantum field theories with special focus on phi^4-theory and quantum electrodynamics.

You will also learn about perturbation theory in terms of Feynman diagrams, with these being developed systematically, along with an introduction to important concepts like regularisation and renormalisation. We’ll apply these tools to the calculation of simple tree-level and one-loop S-matrix elements and cross-sections in phi^4 theory and quantum electroynamics.

#### Astrophysical Plasmas

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.

#### Differential Geometry in Theoretical Physics

This aim of this module is to provide you with a number of advanced mathematical tools from differential geometry, essential for research in modern Theoretical Physics, and apply them to certain physical contexts.

We will introduce the notation of differential forms and explore the geometric aspects of gauge theory. In this geometric setting we will interpret gravity as a guage theory. Another interesting aspect of the module are manifolds, which we will study in detail, leading to the definition of fibre bundles. Finally, we will explore the Dirac and 't Hooft-Polyakov monopoles, as well as Yang-Mills and gravitational instantons, and develop their associated understanding in fibre bundle language.

#### Electromagnetic radiation in astrophysics

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.

#### Electronic structure methods

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.

#### Extrasolar planets and astrophysical discs

This module covers protoplanetary discs, planet formation, and extrasolar planets. 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.

#### Functional Methods in Quantum Field Theory

This module introduces the path integral description of quantum mechanics and applies it to the study of quantum field theory (QFT).

QFT has become a cornerstone of theoretical physics, with a wide range of applications from particle physics (providing the foundations to the standard model) to the description of condensed matter systems (phase transitions).

The module introduces the notions of renormalisation group and effective actions. As a concrete application, the phi^4 theory is discussed in some detail, including the Fisher-Wilson approach to the derivation of the critical exponents.

#### Physical Cosmology

This module covers the essential concepts of modern cosmology, and in particular introduces the student to what has become known as the "cosmological standard model". It discusses the structure and properties of the universe as we observe it today, its evolution and the the underlying physical concepts, and the observations that formed our understanding of the universe.

#### Relativistic Waves and Quantum Fields

This module provides an introduction to Relativistic Quantum Field Theory, which unifies two of last century's greatest discoveries in physics: Special Relativity and Quantum Mechanics.

We will derive and study relativistic wave equations for particles of various spins and analyse the physical interpretations of their solutions. After an introduction to classical field theory, we will discuss the role of symmetries in field theory (including the beautiful Noether's theorem) you will learn the fundamental concepts of quantum field theory, including the quantisation of the free Klein-Gordon and Dirac fields and the derivation of the Feynman propagator. Finally we will introduce and derive a systematic procedure to calculate scattering amplitudes using Feynman diagrams. We will also compute some explicit tree-level scattering amplitudes in a number of simple examples.

#### Relativity and Gravitation

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.

#### Research methods for astrophysics

This module describes the techniques used in scientific research, providing an essential foundation for the skills needed for MSc project work. The emphasis is on how researchers access scientific information. The lectures show how information can be found and evaluated, at a general level and at research level. We will discuss techniques used in scientific writing, including the style required for research papers and an introduction to data archives

#### Supersymmetric Methods in Theoretical Physics

This module starts in 0+1 dimensions with supersymmetric quantum mechanics. In particular, we study the Witten index as an important non-perturbative tool to analyse these theories.

The module then moves on to study various representations in N=2 and N=(2,2) supersymmetric quantum mechanics culminating with a discussion of Berry’s phase in these latter systems.

The final part of the module moves on to supersymmetric quantum field theory in 2+1 dimensions and introduces aspects of the Wilsonian renormalization group, moduli spaces, and duality. The main idea of the module is to get non-trivial insight into strongly coupled quantum systems using symmetry as the guiding principle.

#### The Galaxy

This module considers in detail the basic physical processes that operate in galaxies, using our own Galaxy as an example.

We consider the gravitational dynamics and interactions of star systems, and how their motions can be described mathematically. The contents of the interstellar medium are described, and models are used to represent how the abundances of chemical elements have changed during the lifetime of the Galaxy. We investigate how 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 overview of the structure and characteristics of the Milky Way.

#### The physics of galaxies

Galaxies are the building blocks of the universe. This module applies basic physical ideas to astronomical observations, exploring the properties of galaxies themselves and the evolution of structure in the universe.

The aim of the course is to show how locally-determined physics is applied to the properties of galaxies and clusters of galaxies.

By the end of the course, you should be able to: 1. Categorise the various types of galaxies. 2. Describe how to estimate their properties such as mass and luminosity. 3. Describe how luminosity functions are estimated and explore some of the consequences of the observed functions. 4. Describe the various phenomena observed in normal and active galaxies. 5. Explain these phenomena in terms of simple physical models.

#### Solar system

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 arises from simple physical systems in general. This course 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 course applies basic physical and dynamical principles (such as orbital dynamics and elementary differential equations) needed for the study of the Solar System. However, prior knowledge of these topics is not necessary as they will be introduced as required. As far as possible the course will also include discussions of recent discoveries in planetary science.

#### Stellar structure and evolution

Stars are important constituents of the universe. This course 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.