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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
Article
  • 46 Downloads

Abstract

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Modulus Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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