The spectral Einstein functional and the noncommutative residue for manifolds with boundary

TL;DR

This paper introduces a spectral Einstein functional linked to the Dirac operator on manifolds with boundary and proves a related Kastler-Kalau-Walze type theorem in four dimensions.

Contribution

It defines a new spectral Einstein functional for manifolds with boundary and establishes a Kastler-Kalau-Walze type theorem for it in 4D.

Findings

Defined the spectral Einstein functional for manifolds with boundary

Proved a Kastler-Kalau-Walze type theorem for the functional in 4D

Extended noncommutative residue concepts to boundary cases

Abstract

In this paper, we define the spectral Einstein functional associated with the Dirac operator for manifolds with boundary. And we give the proof of Kastler-Kalau-Walze type theorem for the spectral Einstein functional associated with the Dirac operator on 4-dimensional manifolds with boundary.