Family Index Theorem, Topological properties of Quantum Gauge Theory

The following sections are included:

• Family index theorem of Dirac operator

• Relation among cohomology on orbit space, on connection space and on gauge group

• Topological obstruction of variety degree on gauge group and the Čech-de Rham double complex

• The cocycle density of gauge group and gauge algebra

• Topological properties of 4-dim quantum Yang-Mills theory and θ-vacuum

• 3-dim Yang-Mills theory and topological mass term

• Fermion interaction and quantum anomalies

• Topological interpretation of quantum anomalies

• Notations and Formulae

• Exercise