Anticommutative Integration and Fermi Fields

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.