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Index Theorems for Manifolds with Torsion and Boundary: A Quantum Mechanical Approach
Student-Run Research| Speaker: | Andrew Waldron, Physics, Brandeis University |
| Location: | 693 Kerr |
| Start time: | Wed, Apr 26 2000, 4:10PM |
Description
Index Theorems play an important role in both mathematics and physics
and are a classic example of the deep interplay between the two fields.
We present new results for index theorems on manifolds with boundary and
torsion. The computation is made possible by studying the quantum mechanics of
a supersymmetric spinning particle living on the manifold of interest.
In particular the bulk contribution to the index is calculated via a precise
definition of functional integrals over all possible paths. The results may be
tested via Killing--Yano duality which provides a relation between Dirac
operators on manifolds with and without torsion.