Gauge Theory

This is the web page of the course Gauge Theory, aimed at research PG students in mathematical physics and geometry; although everyone is welcome to attend the lectures.

Outline Syllabus

Basic gauge theory

• Connections on principal bundles
• The YangーMills equations and (anti-)self-duality
• Basic examples: Dirac monopole, BPST instanton

Some complex geometry

• Basic Hodge theory
• Sheaf cohomology

Some transforms

• The FourierーMukai transform
• The ADHM construction
• Nahm's equations

Schedule

Lectures take place on Tuesday at 4:10pm in JCMB 6203 (unless otherwise stated!), in the King's Buildings campus of the University of Edinburgh.

Lecture notes will appear as they are produced. I try not to modify them once they are uploaded, but I do not always succeed due to, for example, the need to refer to equations which were initially unlabelled. (Note to self: label all equations!) There is also a Table of contents which is continuously evolving.

• Tuesday, 7 February 2006
  JCMB 5325
  José Figueroa-O'Farrill
  Connections on principal fibre bundles (1)
• Tuesday, 14 February 2006
  JCMB 5215
  José Figueroa-O'Farrill
  Connections on principal fibre bundles (2)
• Tuesday, 21 February 2006
  JCMB 3317
  José Figueroa-O'Farrill
  Curvature
• Tuesday, 28 February 2006
  JCMB 5327
  José Figueroa-O'Farrill
  The Yang-Mills equations
• Tuesday, 7 March 2006
  Long live the revolution!
• Wednesday, 15 March 2006
  JCMB 5215
  José Figueroa-O'Farrill
  Instantons
• Tuesday, 21 March 2006
  JCMB 5327
  José Figueroa-O'Farrill
  Instanton moduli space
• Tuesday, 25 April 2006
  José Figueroa-O'Farrill
  Instantons and symplectic quotients (1)
• Tuesday, 2 May 2006
  José Figueroa-O'Farrill
  Instantons and symplectic quotients (2)
• Wednesday, 10 May 2006
  JCMB 4312
  José Figueroa-O'Farrill
  Instantons and symplectic quotients (3)

References

This list will be updated periodically. For the list of references used in the notes, click here.

• Tai Tsun Wu and Chen Ning Yang, Concept of nonintegrable phase factors and global formulation of gauge fields
• M Daniel and CM Viallet, The geometrical setting of gauge theories of the Yang-Mills type
• Tohru Eguchi, Peter Gilkey and Andrew Hanson, Gravitation, Gauge Theories and Differential Geometry
• José Figueroa-O'Farrill, Electromagnetic duality for children (for the Dirac monopole)
• José Figueroa-O'Farrill, Gauge theory and the division algebras