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Anticommutative Integration and Fermi Fields

  • P. Krée
Conference paper

Abstract

Let Z be a complex and separable Hilbert space. Norbert Wiener has constructed an isometry of the Symmetrie Fock Space Fock(Z) onto same L2-space. I. Segal and L. Gross have proposed an L2-picture of the antisymmetric Fock space F+(Z) using non-commutative Integration theory. The scope of this lecture is the introduction of a new L2-picture of Fock+ (Z). An explicit formula is given for the intertwining operator; and the result is similar to the corresponding result in the commutative case [3]. Hence a free index ε = ± is introduced: ε = − means “Symmetrie and ε = + means “antisymmetric“. Hence the case of mixed fields with bosons and fermions can be treated by tensor product.

Keywords

Vector Space Inverse Image Hermite Form Grassmann Algebra Symbolic Calculus 
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References

  1. [1]
    F.A. Berezin, The method of second quantization. Academic Press, 1966MATHGoogle Scholar
  2. P. Krée, Séminaire sur les équations aux dérivées partielles en dimension infinie 3e annee 1976–79. Secrétariat mathé-matique de 1’Institut H. PoincaréGoogle Scholar
  3. P. Krée, SxDlutioms faibles d’équations aux dérivées fonctionnelles. Séminaire Lelong Analyse. Lecture notes in mathematics In° 410 - 1972/73, p. 143–181 II 1973/74Google Scholar

Copyright information

© Springer-Verlag/Wien 1980

Authors and Affiliations

  • P. Krée
    • 1
  1. 1.Département de MathématiquesUniversité de Paris VIFrance

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