Boson-Fermion unification implemented by Wick calculus

Abstract

We construct a transformation between Bose Fock space and Fermi Fock space that is super-symmetric in the sense that it converts Boson fields into Fermi fields over a fixed one-particle space h. The transformation the spectral splitting of h into a continuous direct integral of internal spaces. We present a theory of integration on the Fock spaces that is a natural generalization of the theory of quantum stochastic calculus and which we refer to as a Wick calculus.