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arXiv · hep-th/9511151

Index Theory, Gerbes, and Hamiltonian Quantization

Alan Carey·Jouko Mickelsson·Michael Murray
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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.

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Alan Carey, Jouko Mickelsson, Michael Murray. 1995-11-22. Index Theory, Gerbes, and Hamiltonian Quantization. https://doi.org/10.1007/s002200050048

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