Anticommutative Integration and Fermi Fields

  • P. Krée
Conference paper


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.


Vector Space Inverse Image Hermite Form Grassmann Algebra Symbolic Calculus 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations