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Index Theory, Gerbes, and Hamiltonian Quantization | | Alan Carey
; Jouko Mickelsson
; Michael Murray
; | | Date: |
22 Nov 1995 | | Journal: | Commun.Math.Phys. 183 (1997) 707-722 | | Subject: | High Energy Physics - Theory; Differential Geometry | hep-th dg-ga math.DG | | 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. | | Source: | arXiv, hep-th/9511151 | | Services: | Forum | Review | PDF | Favorites | |
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