Unit name | Advanced Quantum Theory |
---|---|
Unit code | MATHM0013 |
Credit points | 10 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 2C (weeks 13 - 18) |
Unit director | Dr. Muller |
Open unit status | Not open |
Pre-requisites |
MATH11005 (Linear Algebra and Geometry), MATH11006 (Analysis 1), MATH 11007 (Calculus 1), either MATH 21900 (Mechanics 2) or MATH 31910 (Mechanics 23), MATH 35500 (Quantum Mechanics), or comparable units. Students will be expected to have attained a degree of mathematical maturity and facility at least at the level of a beginning Level M/7 student. |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Unit aims
The aims of this unit are to introduce and develop some key ideas and techniques of modern quantum theory. These ideas – functional integration, perturbation theory via Feynman diagrams and supersymmetry – are central concepts with extremely wide applicability within modern physics. The aim is to introduce the ideas and also to enable the student to be able to do example calculations with these sophisticated tools. This unit provides essential techniques for any graduate who intends to start research in theoretical or mathematical physics as well as range of other disciplines.
General Description of the Unit
Quantum theory is the fundamental framework within which a vast section of modern physics is cast: this includes atomic, molecular and particle physics as well as condensed matter and statistical physics, and modern quantum chemistry. In recent years it has also had unexpected and deep impact on pure mathematics. Fundamental to applying quantum theory in these areas are the more sophisticated techniques and ideas introduced in this course, namely path integrals, perturbation theory via Feynman diagrams and supersymmetry. These ideas not only allow quantum theory to be applied to these areas but also introduce a raft of concepts which have become a standard language for these fields.
NOTE: This unit is also part of the Oxford-led Taught Course Centre (TCC), and is taken by first- and second-year PhD students in Bristol and its TCC partner departments. The unit has been designed primarily with a postgraduate audience in mind. Undergraduate students should not normally take more than one TCC unit per semester.
Relation to Other Units
Quantum Mechanics and Mechanics 2/23 or equivalent units are prerequisites.
The methods introduced in this course are used in current research in several areas of mathematical and theoretical physics. Units giving an introduction into some of these areas are Statistical Mechanics, Quantum Information, Quantum Chaos, and Random Matrix Theory in Mathematics, and Relativistic Field Theory as well as several courses dealing with Condensed Matter in Physics. The Physics unit Advanced Quantum Physics includes complementary material about the Feynman path integral outside a field theoretical context.
Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/
Learning Objectives
A student successfully completing this unit will be able to:
Transferable Skills
The unit will be delivered through lectures. The lectures will be transmitted over the internet as part of the Taught Course Centre (TCC). The TCC is a consortium of five mathematics departments, including Bath, Bristol, Imperial College, Oxford and Warwick.
The lectures will comprise 15 hrs in total, at not more than 2 hrs per week.
In addition there will be problem sheets and about 3 problem and revision classes.
100% Examination.
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.