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Computational Science Seminar |
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| Category: | Seminar | |
| Date & Time: |
Tuesday , 02/05/2013 from 03:30 PM to 04:30 PM |
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| Location: | LArts Room 218 | |
| Admission: | Free! | |
| Sponsored by: | Provost's Math Seminar and SIAM Chapter | |
| Contact: |
Alfa Heryudono aheryudono@umassd.edu 508-999-8516 |
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| Description: |
Speaker: Dana Fine (Math Dept)
Title: To infinity and beyond! (And back again): A rigorously-defined path integral for supersymmetric quantum mechanics and an easy proof of an index theorem Abstract: The path integrals of quantum physics assume the idea of integration extends to allow integrations over the infinite-dimensional space of paths. Heuristic reasoning suggests that, in certain cases, these infinite-dimensional integrals will localize to finite-dimensional subspaces. If correct, this would imply the equivalence of quantities defined in purely finite-dimensional settings. In this talk, I will describe how to make Feynman's time-slicing approach work to give mathematically precise meaning to the path integrals of N=1 supersymmetric quantum mechanics, and show that the heuristic reasoning proves to be correct in this case. The above-mentioned equivalence is the Gauss-Bonnet-Chern theorem. The convergence of the time-slicing approximation, with bounds on the errors, make this a nice test case for numerical estimates in lattice field theories with fermions. |
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| Additional Info: | UMass Dartmouth Computing | |
