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|Title:||Index Theory, Gerbes, and Hamiltonian Quantization|
|Citation:||Communications in Mathematical Physics, 1997; 183(3):707-722|
|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.|
|Appears in Collections:||Aurora harvest 6|
Pure Mathematics publications
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