Spinors in Geometry and Physics

Math 425 and Physics 498C

S.B. Bradlow and R.G. Leigh

Syllabus (tentative)

Course Abstract

First Day Handouts: 0 , 1 , 2 , 3 .

List of Topics:
  1. (P,M) Historical Remarks
  2. (M) Algebraic Preliminaries
    • Orthogonal groups
    • Spin groups
    • low dimensional examples
    • Clifford Algebras and Representation Theory
  3. (P) Spin in Simple Quantum Systems
  4. (M) Differential Geometry
    • review
    • spin structures on manifolds
    • Stiefel-Whitney classes
  5. (P) Representations used in physics:
    • gamma matrices and Dirac operators in diverse dimensions
    • irreducible spinor representations
  6. (M) More Differential Geometry
    • connections on vector bundles
    • the spin connection
    • Dirac operators
  7. (P) Spinors in curved spacetimes
  8. (M) Index Theorems
  9. (P) Anomalies and Index Theorems
  10. (P) Supersymmetry
  11. (P) Applications
    • General Relativity, positive energy theorems
    • spin manifolds in compactifications of string theories
  12. (M) Seiberg-Witten theory and invariants of 4-manifolds


©1997 R.G. Leigh