ANOMALIES AND INDEX THEOREMS

The following sections are included:

• Axial Anomaly

  • Chiral fermions

  • Quantization of chiral fermions

  • Computation of the axial anomaly: Heat kernel regularization

  • Computation of the axial anomaly: Zeta-function regularization

  • Physical origin of the axial anomaly

  • Axial anomaly and the supersymmetric proof of the index theorem

    • Supersymmetric quantum mechanics

    • Supersymmetric proof of the index theorem: Internal case

• Axial Gauge Anomaly

• Physical Consequences of Anomalies

• Anomalies and Geometry

  • Chern-Weil theory

  • Algebraic approach to anomalies

  • Anomalies and cohomology

• Gravitational Anomalies

  • Supersymmetric proof of the index theorem: External case

  • Index theorems for the classical complexes

    • De Rham complex

    • Dolbeault complex

• Supersymmetric Relativistic Point Particle with Spin

• Appendix: Spin and Spin^c Structures

  • Orientations

  • Spin structures

  • Spin^c structures

• Appendix: Geometric Gauge Fixing Conditions

  • Internal case

  • External case