Math 445 Spring

Spring: Symplectic manifolds and quantization

[This part needs more work]

- Connections on principal bundles
— example: frame bundles of vector bundles
— induced connections on associated bundles
— horizontal distribution implies affine connection
— curvature
- Symplectic manifolds
— Examples: cotangent bundle, coadjoint orbits
— Local theory: Darboux-Weinstein
— Hamiltonian flows
— Classical mechanics
— Moser Rigidity
— prequantization line bundle
- Dirac operators
— Zeta function and analytic torsion for flat vector bundles
— Spectral flow
— Atiyah-Singer and Atiyah-Patodi-Singer
— short discussion of geometric quantization

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License