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.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Author information
Authors and Affiliations
Additional information
Received:
Rights and permissions
About this article
Cite this article
Carey, A., Murray, M. & Mickelsson, J. Index Theory, Gerbes, and Hamiltonian Quantization . Comm Math Phys 183, 707–722 (1997). https://doi.org/10.1007/s002200050048
Issue Date:
DOI: https://doi.org/10.1007/s002200050048