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Dirac operators for compact coadjoint orbits (and for matrix algebras that converge to them?)QMAP Seminar
|Speaker: ||Marc Rieffel, UC Berkeley|
|Location: ||2112 MSB|
|Start time: ||Thu, Apr 2 2009, 3:10PM|
Physicists say that sequences of matrix algebras converge to the 2-sphere or other
coadjoint orbits of compact Lie groups. They then go on to use "vector bundles" for the matrix
algebras that they say correspond to vector bundles on the coadjoint orbits, Dirac operators
for the matrix algebras that correspond to Dirac operators on the coadjoint orbits, Yang-Mills, etc.
I will indicate briefly why physicists want to do this, and how I make sense of the convergence
of matrix algebras to coadjoint orbits. In order to try to understand the situation for Dirac
operators, I have recently studied Dirac operators on coadjoint orbits, emphasizing a global
approach so as to facilitate comparison with possible Dirac operators for matrix algebras.
I will report on what I have found.