A general class of infinite dimensional Dirac operators and path integral representation of their index

Abstract

A general class of infinite dimensional Dirac operators is defined in an abstract Boson-Fermion Fock space and some of their properties are studied. In particular, a path integral representation of their index is established, which gives a topologically invariant integer-valued functional on a space of functionals with values in a Hilbert space. Further, it is shown that, in concrete realizations, the supersymmetric quantum theories associated with the Dirac operators yield the Wess-Zumino models in supersymmetric quantum field theory.