SMSTC Advanced Course: Gauge Theory

Contents and Purpose

Gauge theory plays a fundamental role in modern physics. It is the language in which the standard model of elementary particle physics is formulated. At the same time it has had deep and surprising applications to geometry and topology in four dimensions (Donaldson and Seiberg-Witten theory) and three dimensions (Chern-Simons theory, Floer homology). The purpose of the course is to introduce the basic mathematical concepts and ideas of gauge theory. The course builds to some extent on the existing SMSTC course Geometry and Topology and assumes a basic understanding of manifolds and differential forms. However, necessary tools from Lie groups will be introduced in the first lectures. The course will outline some of the applications of gauge theory in particle physics but will not include a systematic treatment of quantisation.

Delivery

The course will be delivered by a team of lecturers from the Uinversity of Edinburgh, the University of Glasgow and Heriot-Watt University. The lectures can be attended via the SMSTC video facilities at Glasgow (room 104 in the Maths Department) Edinburgh (room 5323 in JCMB) and Heriot-Watt (room T01 in the Colin Maclaurin Building).

All lectures will take place 2-4pm at the dates given below. The material for the lectures will be uploaded as the course progresses.


Date Lecturer Topic Slides Notes Exercises Solutions
Mo 9 September José Figueroa O'Farrill Introduction to Lie Algebras and Lie Groups Slides 1 Exercise 1 Solutions 1
Wed 11 September Bernd Schroers Introduction to Gauge Theory Slides 2 Notes 2 Exercise 2 Solutions 2
Fri 13 September Brendan Owens Fibre Bundles and Connections Slides 3 Exercise 3
Mo 16 September Bernd Schroers and Christian Sämann Monpoles and Instantons Slides 4B Notes 4A (corrected) Exercise 4A
Wed 18 September Christian Sämann ADHM Construction and Instanton Moduli Spaces Slides 5 Exercise 5


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Bernd Schroers
Last modified: 5 September 2013