Determinant Bundles over Grassmannians

  • Jouko Mickelsson
Part of the Plenum Monographs in Nonlinear Physics book series (PMNP)


Denoting by H the Hilbert space of square-integrable Dirac spinor fields on a manifold M, transforming according to a unitary representation p of a gauge group G, we have a linear representation of the group g of gauge transformations in the space H. If ρ is faithful we can consider g as a subgroup of the general linear group GL(H). By constructing representations of GL(H) we automatically obtain representations of g. It turns out that in the case when the dimension d of M is odd, g is contained in a smaller group GL p GL(H) which has the property that it perturbs the subspace H+H consisting of eigenvectors of a Dirac operator belonging to positive eigenvalues, by an operator A for which the trace tr|A|2p exists. The Schatten index depends on the dimension of M. The statement above is true when p(d + 1)/2.


Dirac Operator Central Extension Fredholm Operator Hermitian Form Spin Bundle 
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 Science+Business Media New York 1989

Authors and Affiliations

  • Jouko Mickelsson
    • 1
  1. 1.University of JyväskyläJyväskyläFinland

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