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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
Issue Date: 1997
ISSN: 0010-3616
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
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Pure Mathematics publications

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