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Fermionic Second Quantization and the Geometry of the Restricted Grassmannian

  • Tilmann Wurzbacher
Part of the DMV Seminar Band book series (OWS, volume 31)

Abstract

We explain how fermionic second quantization leads to G res, the restricted Grassmannian of a polarized Hilbert space, and its homogeneous Kähler geometry, and how vice-versa G res encodes - via its holomorphic determinant bundle - the basic ingredients of fermionic second quantization, as, e.g., the fermionic Fock space and the “Schwinger term”. Using this approach we derive a new construction of the universal central extension of U res, the restricted unitary group. Furthermore, we develop the general theory of symplectic manifolds and symplectic actions in infinite dimensions and apply it notably to the U res -action on G res. Finally we construct the determinant bundle on G res functorially using “C*-algebro-geometric methods” naturally arising from the use of CAR-algebras in fermionic second quantization.

Keywords

Line Bundle Frechet Space Determinant Bundle Symplectic Action Canonical Anticommutation Relation 
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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© Springer Basel AG 2001

Authors and Affiliations

  • Tilmann Wurzbacher
    • 1
  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis Pasteur et C.N.R.S.StrasbourgFrance

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