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https://hdl.handle.net/2440/3515
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Type: | Journal article |
Title: | Index Theory, Gerbes, and Hamiltonian Quantization |
Author: | Carey, A. Mickelsson, J. Murray, M. |
Citation: | Communications in Mathematical Physics, 1997; 183(3):707-722 |
Publisher: | SPRINGER VERLAG |
Issue Date: | 1997 |
ISSN: | 0010-3616 1432-0916 |
Abstract: | We give an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and prove that this leads in a simple manner to the known Schwinger terms (Faddeev-Mickelsson cocycle) for the gauge group action. We relate the APS construction to the bundle gerbe approach discussed recently by Carey and Murray, including an explicit computation of the Dixmier-Douady class. An advantage of our method is that it can be applied whenever one has a form of the APS theorem at hand, as in the case of fermions in an external gravitational field. |
DOI: | 10.1007/s002200050048 |
Published version: | http://dx.doi.org/10.1007/s002200050048 |
Appears in Collections: | Aurora harvest 6 Pure Mathematics publications |
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