Superspace formulation of the Chern character of a theta-summable Fredholm module

TL;DR

This paper introduces a supersymmetric approach to the Chern character in entire cyclic cohomology, linking cocycle conditions to supertranslation invariance and providing a path integral for the Dirac operator index.

Contribution

It presents a novel superspace formulation of the Chern character and connects superanalysis with index theory through superfield formalism.

Findings

Cocycle condition relates to supertranslation invariance.

Path integral representation for Dirac operator index.

Supersymmetric formulation enhances understanding of cyclic cohomology.

Abstract

We apply the concepts of superanalysis to present an intrinsically supersymmetric formulation of the Chern character in entire cyclic cohomology. We show that the cocycle condition is closely related to the invariance under supertranslations. Using the formalism of superfields, we find a path integral representation of the index of the generalized Dirac operator.