The spectral Einstein functional for the nonminimal de Rham-Hodge operator

TL;DR

This paper introduces the spectral Einstein functional for a nonminimal de Rham-Hodge operator, computes it on certain manifolds, and provides examples of the associated non-self-adjoint spectral triples.

Contribution

It defines the spectral Einstein functional for non-self-adjoint spectral triples and computes it explicitly for the nonminimal de Rham-Hodge operator on compact manifolds.

Findings

Explicit computation of the spectral Einstein functional.

Examples of non-self-adjoint spectral triples provided.

Extension of spectral triple concepts to non-self-adjoint operators.

Abstract

In this paper, we give the definitions of the non-self-adjoint spectral triple and its spectral Einstein functional. We compute the spectral Einstein functional associated with the nonminimal de Rham-Hodge operator on even-dimensional compact manifolds without boundary. Finally, several examples of the non-self-adjoint spectral triple are listed.