The Fock Bundle of a Dirac Operator and Infinite Grassmannians

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


In the earlier chapters we have studied representations of current algebras in fermionic Fock spaces. A (fermionic) Fock space is determined by a single Dirac operator D. To set up a Fock space we need a splitting of a complex Hilbert space H to the subspaces corresponding to positive and negative frequencies of D. However, in an interacting quantum field theory one really should consider a bundle of Fock spaces parametrized by different Dirac operators. For example, in Yang-Mills theory any smooth vector potential defines a Dirac operator and one must consider the whole bunch of these operators and associated Fock spaces if one wants to describe the interaction of the vector potential with Dirac spinor fields.


Dirac Operator Vector Potential Holomorphic Section Vacuum Vector Trivial Vector Bundle 


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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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