Index Theory, Gerbes, and Hamiltonian Quantization

Details Index Theory, Gerbes, and Hamiltonian Quantization Index Theory, Gerbes, and Hamiltonian Quantization

1995-11-22

arxiv.org/abs/hep-th/9511151v1

Commun.Math.Phys.183:707-722,1997

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, Plain TeX inputting AMSTeX

Scientific paper

10.1007/s002200050048

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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