Letters in Mathematical Physics

, Volume 59, Issue 1, pp 47–60 | Cite as

The Universal Gerbe, Dixmier–Douady Class, and Gauge Theory

  • Alan L. Carey
  • Jouko Mickelsson


We clarify the relation between the Dixmier–Douady class on the space of self-adjoint Fredholm operators (“universal B-field”) and the curvature of determinant bundles over infinite-dimensional Grassmannians. In particular, in the case of Dirac type operators on a three dimensional compact manifold we obtain a simple and explicit expression for both forms.

Gerbes determinant bundles Hamiltonian quantization index theory 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Alan L. Carey
    • 1
  • Jouko Mickelsson
    • 2
  1. 1.Department of MathematicsUniversity of AdelaideAustralia
  2. 2.Royal Institute of TechnologySCFABStockholmSweden

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