On generating functionals for antisymmetric functions and their application in quantum field theory

Abstract

An isomorphism between certain subspaces of the Hilbert spaces of symmetric and antisymmetric n -point functions (or, more generally, symmetric and antisymmetric tensor products of a Hilbert space) is described. It permits a construction of generating functionals for sets of antisymmetric functions. In this way the theory of Hilbert spaces of functional power series as described in [7] and [8] can be extended to the case of antisymmetric coefficients. As an application, the functional representation for the anticommuntation relations is derived. It enables to obtain a functional formulation of quantum field theory also in the antisymmetric case without the use of Grassman algebras.