Communications in Mathematical Physics

, Volume 112, Issue 2, pp 335–341 | Cite as

On the geometry of Dirac determinant bundles in two dimensions

  • Jouko Mickelsson


The gauge and diffeomorphism anomalies are used to define the determinant bundles for the left-handed Dirac operator on a two-dimensional Riemann surface. Three different moduli spaces are studied: (1) the space of vector potentials modulo gauge transformations; (2) the space of vector potentials modulo bundle automorphisms; and, (3) the space of Riemannian metrics modulo diffeomorphisms. Using the methods earlier developed for the studies of affine Kac-Moody groups, natural geometries are constructed for each of the three bundles.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Modulus Space 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Jouko Mickelsson
    • 1
  1. 1.Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of PhysicsMassachusetts Institute of TechnologyCambridgeUSA

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