Theoretical Physics with a Year in Industry MPhys

Core modules:

Fields and Quanta

This module introduces the key concepts of fields and quanta: electric and magnetic fields, the behaviour of electric charges and currents, vectors and densities, potentials, quantum states and their evolution, the probabilistic nature of fundamental physical law, and the breakdown of classical physics. This module will teach you how physics problems relate to these fundamental concepts, and how those concepts are used to construct solutions.

25 credits

Motion and Heat

This module introduces and applies the key concepts of motion and heat: force, equations of motion, phase space, determinism and free will, symmetry and conservation laws, waves and oscillations, coherence and classical frequency-time uncertainty, the laws of thermodynamics, thermal equilibrium, entropy and the arrow of time. You will learn how physics problems relate to these fundamental concepts, and how those concepts are used to construct solutions. You will apply the key concepts to design experiments to test scientific hypotheses. You will develop your data analysis and communication skills and to use different sources of information in your learning. You will work independently and as part of a group, developing a wide variety of study skills that will prepare you for the rest of your degree programme.

25 credits

Optional modules:

Mathematics for Physicists and Astronomers

This module provides the necessary level 1 mathematics for students taking physics and/or astronomy degrees. The following topics will be covered: basic algebra (functions, coordinate systems, algebraic manipulation etc), Taylor and binomial series, common functions of one variable, differentiation and integration techniques, basic complex numbers, first and second order differential equations, vector calculus, properties and applications of matrices and elementary probability theory.

30 credits

Supplementary Mathematics for Theoretical Physicists

This module provides the necessary supplementary mathematics for theoretical physics students taking level 1 mathematics modules. The following topics will be covered: consolidate previous knowledge of vectors; introduce the students to vector calculus; elementary probability theory; ensure that the students have a thorough knowledge of how to apply mathematical tools to physical problems.

10 credits

Mathematics Core 1

The module explores topics in mathematics which will be used throughout many degree programmes. The module will consider techniques for solving equations, special functions, calculus (differentiation and integration), differential equations, Taylor series, complex numbers and finite and infinite series.

20 credits

Mathematics Core II

The module continues the study of core mathematical topics begun in MS4F1015, which will be used throughout many degree programmes. The module will discuss 2-dimensional co-ordinate geometry, discussing the theory of matrices geometrically and algebraically, and will define and evaluate derivatives and integrals for functions which depend on more than one variable, with an emphasis on functions of two variables.

20 credits

Introduction to Astrophysics

One of four half-modules forming the Level-1 Astronomy course, PHY104 aims to equip students with a basic understanding of the important physical concepts and techniques involved in astronomy with an emphasis on how fundamental results can be derived from fairly simple observations. The module consists of three sections:

(i) Basic Concepts, Fluxes, Temperatures and Magnitudes;

(ii) Astronomical Spectroscopy;

(iii) Gravitational Astrophysics.

Parts (i), (ii) and (iii) each comprise some six lectures. The lectures are supported by problems classes, in which you will learn to apply lecture material to the solution of numerical problems.

10 credits

The Solar System

One of the four half-modules forming the Level 1 astronomy course, but may also be taken as a stand-alone module. PHY106 covers the elements of the Solar System: the Sun, planets, moons and minor bodies. What are their structures and compositions, and what dothey tell us about the formation and history of the Solar System?

10 credits

Our Evolving Universe

The course provides a general overview of astronomy suitable for those with no previous experience of the subject. The principal topics covered are (1) how we deduce useful physical parameters from observed quantities, (2) the structure and evolution of stars, (3) the structure of the Milky Way, and the classification, structure and evolution of galaxies in general, (4) an introduction to cosmology and (5) extrasolar plantets and an introduction to astrobiology. All topics are treated in a descriptive manner with minimal mathematics.

10 credits

Frontiers of Physics

This pair of 10-credit modules aims to introduce research-inspired material into the level 1 physics curriculum. Each module includes three short courses on research-based topics taught by an academic who is actively involved in the research. The individual courses will be regularly reviewed to ensure that the material is up to date and includes current areas of investigation. The module aims to show that cutting-edge physics research is often underpinned by basic concepts covered in A level and 1st year physics courses.

10 credits

The Physics of Sustainable Energy

The module will cover the physics of sustainable energy. It includes discussions framed by the book `Sustainable Energy without the Hot Air' by D MacKay and will cover current energy requirements and what energy could potentially be provided by the various forms of renewable energy. The course will commence with a discussion of the basic physics of energy, power and work and the conversion of energy from one form to another. We examine in detail the history of global energy useage and how we produce and use energy in the UK. We will then explore the impacts that this energy use has on the biosphere and climate and the public perception of such processes. The course will then focus on the energy contenet of objects and processes we take for granted and will then move on to means by which we can produce energy using renewable technologies, such as wind, wave, solar, biofuels etc. We will also examine nuclear (fusion and fission) energy and will discuss their principles and practical implementation. Finally, we will consider solutions to our energy needs, including transportation, energy conservation, carbon capture and geoengineering.

10 credits

Physics of Living Systems 2

The aim is to introduce biomechanical descriptions of the human body. We look at its structure and its performance as a physical machine. The structural characteristics of human bones and tissue are investigated, together with the mechanical functions of the skeleton and musculature. Simple fluid dynamic characteristics of the body are introduced, including descriptions of blood-flow in the arteries and veins and air-flow in the lungs.

10 credits

Introduction to Electric and Electronic Circuits

This module introduces the concepts and analytical tools for predicting the behaviour of combinations of passive circuit elements, resistance, capacitance and inductance driven by ideal voltage and/or current sources which may be ac or dc sources. The ideas involved are important not only from the point of view of modelling real electronic circuits but also because many complicated processes in biology, medicine and mechanical engineering are themselves modelled by electric circuits. The passive ideas are extended to active electronic components; diodes, transistors and operational amplifiers and the circuits in which these devices are used. Transformers, magnetics and dc motors are also covered.

20 credits

Core modules:

Classical and Quantum Physics for Theoretical Physics

This module provides the core level 2 physics content for the theoretical degrees. It integrates physics content with supporting mathematics and computational/practical work. Transferable skills are covered via different presentation modes for course work. A further item is employability. The module also contains one or more items of group work. Physics topics covered are classical physics and oscillations, thermal physics, quantum mechanics, properties of matter and electromagnetism. Mathematics topics are Fourier techniques and partial differential equations. Both mathematical topics are applied to a range of the physics covered and are integrated with aspects of the computational work. The module is assessed via four standard exams (15% each), three topical and one integrative covering all the taught material, and course work (40%). Students must develop and pass a portfolio to pass the module.

70 credits

Programming in Python

Teaching computer programming is a core aspect to our degree courses and is required by our accreditation body, the Institute of Physics. Python is a widely-available programming language that can be used to design powerful computer programmes suitable for scientific applications. In addition, Python is flexible, robust and is relatively easy to learn compared to other contemporary programming language. Python is also used widely in the computing industry and in research. The aim of this module is to teach the key elements of Python programming to enable students to design programs to perform tasks ranging from computational and numerical physics to data analysis and visualisation.

10 credits

Special Relativity & Subatomic Physics

Special relativity is a key foundation of modern physics, particularly in the contexts of particle physics and astrophysics where E = mc2 and relativistic speeds are crucial concepts. In this module, the fundamental principles of special relativity will be explained, emphasising the energy-momentum four-vector and its applications to particle collisions and decays. Applications to nuclear physics include nuclear mass and binding energy, radioactive decay, nuclear reactions, nuclear fission and fusion. We will also cover the structure of the nucleus (liquid drop model and an introduction to the shell model).

10 credits

Optional modules:

Advanced Calculus and Linear Algebra

Advanced Calculus and Linear Algebra are basic to most further work in pure and applied mathematics and to much of statistics. This course provides the basic tools and techniques and includes sufficient theory to enable the methods to be used in situations not covered in the course.
The material in this course is essential for further study in mathematics and statistics.

20 credits

Differential Equations

The module aims at developing a core set of advanced mathematical techniques essential to the study of applied mathematics. Topics include the qualitative analysis of ordinary differential equations, solutions of second order linear ordinary differential equations with variable coefficients, first order and second order partial differential equations, the method of characteristics and the method of separation of variables.

20 credits

Aspects of Medical Imaging and Technology

This module provides an introduction to medical technology, with a particular bias towards ionising and non-ionising electromagnetic radiation and its diagnostic role in medicine. The module begins with the generation and behaviour of electromagnetic waves and the breadth of technological application across the electomagnetic spectrum. This extends from magnetic resonance imaging at low energies to high energy photons in X-ray systems. The importance of radiation in diagnosis is acknowledged by discussion of imaging theory and primary imaging modalities, such as planar radiography and CT. The therapeutic role is examined by a brief consideration of radiotherapy.

10 credits

Astronomical Spectroscopy

This level 2 module provides an overview of astronomical spectroscopy for astrophysics dual students, covering how spectrographs work, the nature of spectra, atomic physics relevant to astronomical spectroscopy, line broadening mechanisms (natural, pressure, thermal) and the Curve of Growth for the determination of ionic abundances in stellar atmospheres, plus spectral diagnostics of ionized nebulae. Content from lectures are reinforced through an exercise involving specialist astronomical software relating to nebular diagnostics, plus the manipulation of stellar spectroscopic datasets using the programming language Python for the calculation of ionic abundances.

10 credits

Detection of Fundamental Particles

The Standard Model of particle physics is one of the great success stories of late 20th century physics - but how do we obtain the data needed to construct and test this model? In this module, we will explore how typical experiments in different branches of particle physics are designed to extract the maximum possible amount of data from the interactions that they observe. This will be supplemented by laboratory and computational exercises in which students try out some of these techniques themselves.

10 credits

Galaxies

This Level 2 Astronomy half-module aims to provide a comprehensive introduction to galaxies. It consists of six parts: (i) astronomical distance determination and galaxy classification; (ii) the properties of the main stellar and a gas components of our Milky Way galaxy, and its local environment; (iii) the properties of spiral galaxies; (iv) the properties of elliptical galaxies; (v) active galaxies; (vi) galaxy evolution. Students' presentation and research skills are developed through a 2500 word essay assignment.

10 credits

Mechanics and Fluids

This module extends the Newtonian mechanics studied in MAS112. The main topics treated are (i) extensions of the work-energy principle and conservation of energy, (ii) a full treatment of planetary and satellite motion, (iii) the elements of rigid body motion, and (iv) inviscid (frictionless) fluid motions. The course is a prerequisite for students wishing to pursue higher level modules in fluid mechanics.

10 credits

Physics of Materials

This module provides an introduction to the physical properties of materials. Subjects covered include properties of liquids (surface tension, viscosity etc), solids (elastic properties, mechanical properties etc) and soft condensed matter.

10 credits

Stellar Structure and Evolution

The module aims to provide an understanding of the physical processes occurring in stars and responsible for their internal structure and evolution from the main sequence to white dwarfs, neutron stars stars and black holes. It builds on Introduction to Astrophysics (PHY104) and seeks to explain the evolutionary phenomena described in Our Evolving Universe (PHY111).

10 credits

The Physics of Music

This module will provide an introduction to the physics of music building on physics covered in year 1 and semester 2 of year 2. The module will include the following topics: Recap of oscillations, waves and resonance, the human voice, physics of tuned and untuned percussion, musical pitch and timbre, Fourier analysis, musical scales, physics of stringed instruments, physics of wind instruments, electric instruments (based on electro-magnetic pickups and piezoelectric transducers), synthesizers (analogue and digital), sound recording and reproduction (analogue and digital), myths, legends, folklore and pseudoscience in acoustics.

10 credits

Physics with Labview

The module will teach Labview software, and allow students to experiment with instrumentation and basic electronics. These skills will be useful in further years of study, particularly with regard to the Level 3 and 4 projects. These skills are also useful in future employment in both academic and industrial science and engineering where being able to develop laboratory instrumentation to solve experimental problems will be highly desirable.

10 credits

Core modules:

Advanced Electrodynamics

This module gives a detailed mathematical foundation for modern electrodynamics, starting from Maxwell's equations, charge conservation and the wave equation, to gauge invariance, waveguides, cavities and antennas. After a brief recap of vector calculus, we explore the role of the scalar and vector potential, the multi-pole expansion of the field, the Poisson and Laplace equations, energy and momentum conservation of the fields, and Green's functions. We conclude with a relativistic treatment of the fields.

10 credits

Atomic and Laser Physics

This module covers the physics of atoms and lasers at an intermediate level. The course begins with the solution of the Schrodinger equation for the hydrogen atom and the atomic wave functions that emerge from it. It then covers atomic selection rules, spectral fine structure and the effects of external fields. The spectra of selected multi-electron atoms are described. The basic operation of the laser is then covered by introducing the concepts of stimulated emission and population inversion. The course concludes with a description of common lasers and their applications.

10 credits

Further Quantum Mechanics

This module builds on the quantum mechanics learned in the perquisites PHY250 and PHY251. The Heisenberg matrix formulation of the theory is developed from the Schrodinger wave picture. Approximately methods (perturbation theory and variational method) are derived and applied. Methods for solving time dependent problems are developed. Problems involving magnetic fields and spin are treated. Many particle wavefunctions for fermions and bosons are introduced.

10 credits

Mathematical Physics

Linear algebra: matrices and vectors; eigenvalue problems; matrix diagonalisation; vector spaces; transformation of basis; rotation matrices; tensors; Lie groups; Noether's theorem. Complex analysis: analytic functions; contour integration; Cauchy theorem; Taylor and Laurent series; residue theorem; application to evaluating integrals; Kronig-Kramers relations; conformal mapping; application to solving Laplace's equation.

10 credits

Nuclear Physics

This half-module Level 3 Physics course aims to study the general properties of nuclei, to examine the characteristics of the nuclear force, to introduce the principal models of the nucleus, to discuss radioactivity, to study nuclear reactions, in particular fission and fusion, and to develop problem solving skills in all these areas. The motivation is that nuclear processes play a fundamental role in the physical world, in the origin of the universe, in the creation of the chemical elements, as the energy source of the stars and in the basic constituents of matter - plus the best of all motives - curiosity.

10 credits

Particle Physics

This Level 3 Physics half module introduces students to the exciting field of modern particle physics. It provides the mathematical tools of relativistic kinematics, enabling them to study interactions and decays and evaluate scattering form factors. Particles are classified as fermions - the constituents of matter (quarks and leptons) - or as bosons, the propagators of field. The four fundamental interactions are outlined. Three are studied in detail: Feynman diagrams are introduced to describe higher order quantum electrodynamics; weak interactions are discussed from beta decay to high energy electroweak unification; strong interactions, binding quarks into hadrons, are presented with the experimental evidence for colour. The role symmetry plays in the allowed particles and their interactions is emphasised.

10 credits

Problem Solving and Advanced Skills in Physics

This half-module seeks to provide insight and support to the Level 3 Physics programme as a whole. Lectures and tutorials will build upon previous skills developed involving data analysis and errors, information retrieval and scientific writing. Problem classes are directed to impart a broad, coherent and critical grasp of the fundamentals of Physics. Students are encouraged to attempt unfamiliar problems, extract the essentials, and so obtain quick, rough but sound solutions. The module involves group work and is assessed by means of class tests and written examinations. The latter are designed to test basic concepts of Physics and the ability to apply them to unrehearsed situations.

10 credits

Solid State Physics

Covering the electronic properties of solids, this module details the classification of solids into conductors, semiconductors and insulators, the free electron model, the origin of electronic band structure, the fundamental electronic properties of conductors and semiconductors, carrier statistics, experimental techniques used to study carriers in a solid, and the classification and physics of the principal types of magnetism.

10 credits

Statistical Physics

Statistical Physics is the derivation of the thermal properties of matter using the under-lying microscopic Hamiltonians. The aims of this course are to introduce the techniques of Statistical Mechanics, and to use them to describe a wide variety of phenomena from physics, chemistry and astronomy.

10 credits

Optional modules:

Industrial Group Project in Physics

PHY346 provides students with an industrial project where team working, planning, time management; presentation and report writing are integrated with science problem solving. The industrial client poses a problem that a group work on over two semesters to resolve. Interim and final presentations are made to the client and academic supervisors. Project work may use laboratory measurement and computational approaches as well as referencing leading research literature.

20 credits

Microscopy and Spectroscopy Laboratory

This module will develop transferrable skills that will be useful in further experimental project work and industrial science and technology roles. Students will gain hands-on experience using a range of sophisticated experimental techniques to explore physics research and real world context-based questions. Atomic force microscopy (AFM), optical and gamma-ray spectroscopies, as well as associated techniques such as ellipsometry will be used. Students will undertake a series of experiments, supported by lectures, in semester one and conduct an open-ended project utilising the techniques in semester two.

20 credits

Physics Education and Outreach

This 20-credit Extended Project unit is intended primarily for students considering a career in teaching, but may also be of interest to those wishing to pursue careers in science communication in general. The first half of the unit will introduce a range of topics including theory of learning and teaching, skills such as video editing, physics in the National Curriculum, and a range of hands-on exercises in science teaching and communication. Students will undertake a range of assignments related to the taught material, which may include lesson observations in schools, making videos or podcasts, radio broadcasts, writing popular articles or creating resources for schools. The second half consists of a 10-credit project: a wide range of schools and outreach-related topics are available.

Note that admission to this unit is subject to an interview and a DBS check. This is because parts of the unit require students to visit schools and interact with pupils.

20 credits

Advanced Programming in Python

Python is a widely-available programming language that can be used to design powerful computer programmes suitable for scientific applications. Python is also used widely in the computing industry and in research. This module builds on the basic introduction provided in PHY235/PHY241 by introducing advanced concepts such as defensive programming, classes, program design and optimisation. This teaching will be underpinned with a series of projects which will furnish the students with the ability to design complex Python scripts to address a wide variety of problems including those involving analysis of `big data with emphasis on presentation of results using advanced visualisation methods.

10 credits

Continuum Mechanics

Continuum mechanics is concerned with the mechanical behaviour of solids and fluids which change their shape when forces are applied. For example, rubber extends when pulled but behaves elastically returning to its original shape when the forces are removed. Water starts to move when the external pressure is applied. This module aims to introduce the basic kinematic and mechanical ideas needed to model deformable materials and fluids mathematically. They are needed to develop theories which describe elastic solids and fluids like water. In this course, a theory for solids which behave elastically under small deformations is developed. This theory is also used in seismology to discuss wave propagation in the Earth. An introduction in theory of ideal and viscous, incompressible and compressible fluids is given. The theory is used to solve simple problems. In particular, the propagation of sound waves in the air is studied.

10 credits

Dark Matter and the Universe

Dark matter, though still unidentified and not yet directly detected, is established as a major constituent of the universe according to modern cosmology. In this course, we will review the astrophysical and cosmological evidence for the existence of dark matter, critically assess the various candidates that have been put forward, and discuss direct detection methods for the two most popular candidates: WIMPs and axions. The course has a multidisciplinary flavour combining work in astronomy, particle physics, solid state physics, detector technology and philosophy, encouraging development of skills in all these.

10 credits

Differential Geometry

What is differential geometry? In short, it is the study of geometric objects using calculus. In this introductory course, the geometric objects of our concern are curves and surfaces. Besides calculating such familiar quantities as lengths, angles and areas, much of our focus is on how to measure the 'curvature' of a geometric object. The story is relatively simple for curves, but naturally becomes more involved for surfaces - and more interesting too.

10 credits

Fluid Mechanics I

The way in which fluids move is of immense practical importance; the most obvious examples of this are air and water, but there are many others such as lubricants in engines. Moreover, the scientific principles and mathematical techniques needed to explain fluid motion are of intrinsic interest. This module builds on Level 2 work (MAS222 Differential Equations; MAS280 Mechanics and Fluids). The first step is to derive the equation (Navier-Stokes) governing the motions of most common fluids. This serves as a basis for the remainder of MAS320, with the main addition to MAS280 being that it covers viscous (frictional) fluids.

10 credits

History of Astronomy

The module aims to provide an introduction to the historical development of modern astronomy. After a brief chronological overview and a discussion of the scientific status of astronomy and the philosophy of science in general, the course is divided into a series of thematic topics addressed in roughly chronological order. We will focus on the nature of discovery in astronomy, in particular the interplay between theory and observation, the role of technological advances, and the relationship between astronomy and physics.

10 credits

Introduction to Cosmology

Cosmology is the science of the whole Universe: its past history, present structure and future evolution. In this module we discuss how our understanding of cosmology has developed over time, and study the observed properties of the universe, particularly the rate of expansion, the chemical composition, and the nature of the cosmic microwave background, can be used to constrain theoretical models and obtain value for the parameters of the now-standard Hot Big Bang cosmological model.

10 credits

Mathematical Biology

This module provides an introduction to the mathematical modelling of the dynamics of biological populations. The emphasis will be on deterministic models based on systems of differential equations that encode population birth and death rates. Examples will be drawn from a range of different dynamic biological populations, from the species level down to the dynamics of molecular populations within cells. Central to the module will be the dynamic consequences of feedback interactions within the populations. In cases where explicit solutions are not readily obtainable, techniques that give a qualitative picture of the model dynamics (including numerical simulation) will be used.

10 credits

Mathematical modelling of natural systems

Mathematical modelling enables insight in to a wide range of scientific problems. This module will provide a practical introduction to techniques for modelling natural systems. Students will learn how to construct, analyse and interpret mathematical models, using a combination of differential equations, scientific computing and mathematical reasoning. Students will learn the art of mathematical modelling: translating a scientific problem into a mathematical model, identifying and using appropriate mathematical tools to analyse the model, and finally relating the significance of the mathematical results back to the original problem. Study systems will be drawn from throughout the environmental and life sciences.

10 credits

Nuclear Astrophysics

The aims of this Level 3 Astronomy module are:

1) To examine the evidence for the present distribution of the chemical elements in the Universe.

2) To study the various nuclear processes that have led to the evolution of these elemental abundances.

3) To discuss the possible astrophysical sites where these elements are produced.

10 credits

Physical Computing

Digital circuits underpin our modern lives, including the acquisition and processing of data for science. In this course we will study the fundamental building blocks of digital processing circuits and computers. We will learn to describe circuits using the language VHDL, and how to program computers using the hardware-oriented high level language C. We will build interesting and useful digital architectures, and apply the skills we have acquired in laboratory exercises.

10 credits

Astrobiology

Is anybody out there? In this module we explore how we hope to find alien life in the near future and discuss what this might be like and where we should be looking. We critically examine ideas about the frequency of life, advanced life, and technological civilisations in the universe.

10 credits

Research project in Physics

The aim of this 20 credit module is to provide an opportunity for students to exercise and develop their skills and ability to undertake independent, albeit closely supervised, research in physics. A very wide selection of projects is provided, often arising from current research in the Department. Many are practical, others are essentially theoretical or interpretative or require the development of and running of computer programmes designed to simulate a variety of physical phenomena. Most projects are collaborative and encourage students to work in pairs. Assessment is based on individual written reports and oral examinations. These provide exercise in presentational skills.

20 credits

Semiconductor Physics and Technology

This module builds on the core solid state physics modules to provide an introduction to semiconductor electronic and opto-electronic devices and modern developments in crystal growth to produce low dimensional semiconductor structures (quantum wells, wires and dots). Band structure engineering, the main physical properties and a number of applications of low dimensional semiconductor structures are covered.

10 credits

The Physics of Soft Condensed Matter

Soft condensed matter is a generic name for a class of materials that play a crucial role in technology as well as providing fascinating and timely scientific problems. These complex materials are typified by polymers, gels and colloidal dispersions, whose properties often seem intermediate between ordinary liquids and solids. Familiar examples from everyday life include plastics, soaps and detergents, foodstuffs, and indeed the material from which living organisms are constructed. Only relatively recently has it been realised that despite the complexity of these materials elegant and simple physical principles often underlie their behaviour; this course provides an introduction to these principles.

10 credits

Quantum Information Laboratory

This predominantly laboratory-based module provides a foundation in quantum optics experiments and associated theory. The quantum nature of light will be studied in core experiments involving single photon generation and detection, measurements of photon statistics and photon interference. Experimental activities will be supported by a series of lectures and problems classes. The link with quantum information research is made through research seminars from university research groups and companies, plus a 'journal club' where key scientific papers are presented and discussed. Transferable skills acquired will prepare students for higher study and employment in industries involving quantum technologies.

20 credits

Core modules:

Research project

Students will undertake a supervised research project during the whole of the 4th year of an MPhys degree, applying their scientific knowledge to a range of research problems experimental and/or theoretical projects spanning the research expertise of the Department. Along with applying their knowledge, students will manage their project, ensuring that they develop skills in time management, project planning, scientific record keeping, information retrieval and analysis from scientific and other technical information sources.

60 credits

Advanced Quantum Mechanics

This module presents modern quantum mechanics with applications in quantum information and particle physics. After introducing the basic postulates, the theory of mixed states is developed, and we discuss composite systems and entanglement. Quantum teleportation is used as an example to illustrate these concepts. Next, we develop the theory of angular momentum, examples of which include spin and isospin, and the method for calculating Clebsch-Gordan coefficients is presented. Next, we discuss the relativistic extension of quantum mechanics. The Klein-Gordon and Dirac equations are derived and solved, and we give the equation of motion of a relativistic electron in a classical electromagnetic field. Finally, we explore some topics in quantum field theory, such as the Lagrangian formalism, scattering and Feynman diagrams, and modern gauge field theory.

10 credits

Optional modules

Analytical Dynamics and Classical Field Theory

Newton formulated his famous laws of mechanics in the late 17th century. Later, mathematicians like Lagrange, Hamilton and Jacobi discovered that underlying Newton's work are wonderful mathematical structures. In the first semester we discuss this work, its influence on the subsequent formulation of field theory, and Noethers theorem relating symmetries and conservation laws.
In the second semester, Einsteins theory of gravity, General Relativity, will be introduced, preceded by mathematical tools such as covariant derivatives and curvature tensors. Einstein's field equations, and two famous solutions, will be derived. Two classic experimental tests of General Relativity will be discussed.

20 credits

Topics in Advanced Fluid Mechanics

This module aims to describe advanced mathematical handling of fluid equations in an easily accessible fashion. A number of topics are treated in connection with the mathematical modelling of formation of the (near-)singular structures with concentrated vorticity in inviscid flows. After discussing prototype problems in one and two dimensions, the three-dimensional flows in terms of vortex dynamics are described. Key mathematical tools, for example, singular integrals and calculus inequalities, are explained during the unit in a self-contained manner. Candidates are directed to read key original papers on some topics to deepen their understanding.

20 credits

Advanced Particle Physics

The main aim of the unit is to give a formal overview of modern particle physics. The mathematical foundations of Quantum Field Theory and of the Standard Model will be introduced. The theoretical formulation will be complemented by examples of experimental results from the Large Hadron Collider and Neutrino experiments. The unit aims to introduce students to the following topics:
- A brief introduction to particle physics and a review of special relativity and quantum mechanics
- The Dirac Equation
- Quantum electrodynamics and quantum chromo-dynamics
- The Standard Model
- The Higgs boson
- Neutrino oscillations 
- Beyond the Standard Model physics

10 credits

An Introduction to General Relativity

This module introduces coordinate systems and transformations in Euclidean space. The principles of special relativity are reviewed, with emphasis on the coordinate transformations between systems moving at constant velocities. Our discussion of general relativity begins with an introduction to the principle of equivalence. We introduce the Christoffel symbols and the curvature tensors. We study examples of phenomena affected by general relativity, the rate of clocks and the redshift and bending of light in a gravitational field. Finally, we examine space time in the vicinity of the event horizon, the geometry of a non-spinning black hole, and the geometry of wormholes.

10 credits

Biological Physics

This module will introduce students to biological physics, that is, the application of principles and tools from physics to biological systems. Biological materials are often soft condensed matter with properties between those of simple liquids and solids. In addition biological matter is usually out of equilibrium due to internal biochemical sources of energy. Students will begin to explore the world of biological cells and biopolymer macromolecules, such as DNA. They will see how physics can help understand biological systems through mathematical models and experimental imaging techniques and how this can lead to new physics and applications in biology.

10 credits

Dark Matter and the Universe

Dark matter, though still unidentified and not yet directly detected, is established as a major constituent of the universe according to modern cosmology. In this course, we will review the astrophysical and cosmological evidence for the existence of dark matter, critically assess the various candidates that have been put forward, and discuss direct detection methods for the two most popular candidates: WIMPs and axions. The course has a multidisciplinary flavour combining work in astronomy, particle physics, solid state physics, detector technology and philosophy, encouraging development of skills in all these.

10 credits

History of Astronomy

The module aims to provide an introduction to the historical development of modern astronomy. After a brief chronological overview and a discussion of the scientific status of astronomy and the philosophy of science in general, the course is divided into a series of thematic topics addressed in roughly chronological order. We will focus on the nature of discovery in astronomy, in particular the interplay between theory and observation, the role of technological advances, and the relationship between astronomy and physics.

10 credits

Introduction to Cosmology

The module will cover advanced astrophysics topics involving observations and theory of star and planet formation, plus the evolution of low, intermediate and high mass single stars, close binary evolution including their end states (white dwarfs, neutron stars, black holes), supernovae and gamma ray bursts.

10 credits

Magnetic Resonance: Principles and Applications

The module will provide an overview of the basics of magnetic resonance, and then consider its applications in systems ranging from macroscopic living organisms, as in magnetic resonance imaging (MRI) widely used in hospitals, to nano-scale systems where control of single or a few spins is now possible and can also be used for nano-imaging. Special attention will be paid to recent advances in solid-state nano-NMR and the control of single electron spins in solid state nano-systems using spin resonance techniques.

10 credits

Magnetohydrodynamics

Magnetohydrodynamics has been successfully applied to a number of astrophysical problems (eg to problems in Solar Magnetospheric Physics), as well as to problems related to laboratory physics, especially to fusion devices. This module gives an introduction to classical magnetohydrodynamics. Students will get familar with the system of magnetohydrodynamic equations and main theorems that follow from this system (e.g. conservation laws, anti-dynamo theorem). They will study the simplest magnetic equilibrium configurations, propagation of linear waves, and magnetohydrodynamic stability. The final part of the module provides an introduction to the theory of magnetic dynamo

10 credits

Mathematical modelling of natural systems (Advanced)

Mathematical modelling enables insight in to a wide range of scientific problems. This module will provide a practical introduction to techniques for modelling natural systems. Students will learn how to construct, analyse and interpret mathematical models, using a combination of differential equations, scientific computing and mathematical reasoning. Students will learn the art of mathematical modelling: translating a scientific problem into a mathematical model, identifying and using appropriate mathematical tools to analyse the model, and finally relating the significance of the mathematical results back to the original problem. Study systems will be drawn from throughout the environmental and life sciences.

10 credits

Optical Properties of Solids

This course covers the optical physics of solid state materials. It begins with the classical description of optical propagation. It then covers the treatment of absorption and luminescence by quantum theory, and the modifications caused by excitonic effects. The phenomena are illustrated by discussing the optical properties of insulators, semiconductors, and metals. The infrared properties of ionic systems are then discussed, and the course concludes with a brief introduction to nonlinear crystals.

10 credits

Particle Astrophysics

The LHC accelerates protons to kinetic energies of up to 7000 times their rest mass - a huge technological achievement. Yet, every second, over 500 million particles with energies greater than this collide with the Earth. Where do these particles come from, and how are they accelerated to these astonishing energies? These are, in fact, still open questions in astrophysics. In this module, we will look at the observational evidence for particle acceleration in astrophysical objects, the mechanisms available to accelerate particles, and some of the likely sources, including supernovae and supernova remnants, neutron stars, and active galaxies

10 credits

Physics Communication and Impact

This module explores how physics ideas and concepts can be communicated to non-specialist audiences. We discuss how to design a communication, and the importance of knowing the purpose, message, and audience to pick the right medium and narrative. The main goal is to design your own communications to target particular audiences with a particular purpose and message. We will also discuss what impact is and how to assess it, analyse other people's communications, and consider aspects of communication, such as accessibility and some communication theory.

10 credits

Physics in an Enterprise Culture

This is a seminar and workshop based course with a high level of student centred learning. The unit will introduce students to the methods and skills associated with innovation, business planning, costing and marketing. It will broaden students understanding of the mechanics of project planning and research commercialisation. The course is divided into two components:

Part 1: Coming up with ideas. Students will take part in guest lectures and workshop classes to explore different ideas for business. They will learn about the innovation process and what makes a sucessful business. They will finish part 1 by submitting a draft business proposal that will be reviewed by academic staff and student peers and feedback will be given.

Part 2: Armed with the feedback from part 1 students will refine thier ideas and work towards a final pitch for thier business. Further support will be given to students to develop a costing of the idea.

10 credits

Semiconductor Physics and Technology

This module builds on the core solid state physics modules to provide an introduction to semiconductor electronic and opto-electronic devices and modern developments in crystal growth to produce low dimensional semiconductor structures (quantum wells, wires and dots). Band structure engineering, the main physical properties and a number of applications of low dimensional semiconductor structures are covered.

10 credits

The Development of Particle Physics

The module describes the development of several crucial concepts in particle physics, emphasising the role and significance of experiments. Students are encouraged to work from the original literature (the recommended text includes reprints of key papers). The module focuses not only on the particle physics issues involved, but also on research methodology - the design of experiments, the critical interpretation of data, the role of theory, etc. Topics covered include the discoveries of the neutron, the positron and the neutrino, experimental evidence for quarks and gluons, the neutral kaon system, CP violation etc.

10 credits

The Physics of Soft Condensed Matter

Soft condensed matter is a generic name for a class of materials that play a crucial role in technology as well as providing fascinating and timely scientific problems. These complex materials are typified by polymers, gels and colloidal dispersions, whose properties often seem intermediate between ordinary liquids and solids. Familiar examples from everyday life include plastics, soaps and detergents, foodstuffs, and indeed the material from which living organisms are constructed. Only relatively recently has it been realised that despite the complexity of these materials elegant and simple physical principles often underlie their behaviour; this course provides an introduction to these principles.

10 credits