Classical Topology and Quantum Phases
Prof. A.P. Balachandran
Syracuse University, USA.
03, 04, 10 & 11-01-05

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Abstract

In the 4 lectures, I plan to start with very elementary physical examples like the charge-monopole system and particles of fixed spin and show how phases of wave functions can play a very important role in quantum theory. The discussion naturally leads one to the concept of fibre bundles. I plan to explain this concept by the above examples and perhaps also by examples drawn from molecular physics. However I want to leave the later parts of these lectures a bit open and develop them according to student response and time.

The material I will use is covered in the first few chapters of the two books: 1) Gauge Theory and Fibre Bundles (Springer-Verlag) and 2) Classical Topology and Quantum States (World-Scientific). Both these books are authored by me and coworkers.