Nonminimal De Rham-Hodge Operators and Non-commutative Residue

TL;DR

This paper establishes a Kastler-Kalau-Walze type theorem for nonminimal de Rham-Hodge operators on compact manifolds with boundary, linking operator theory to gravitational action in four dimensions.

Contribution

It introduces a new theorem connecting nonminimal de Rham-Hodge operators with gravitational action, providing operator-theoretic explanations for four-dimensional manifolds with flat boundary.

Findings

Derived a Kastler-Kalau-Walze type theorem for nonminimal de Rham-Hodge operators.

Provided two operator-theoretic explanations of gravitational action.

Applied results to four-dimensional compact manifolds with flat boundary.

Abstract

In this paper, we get a Kastler-Kalau-Walze type theorem associated to nonminimal de Rham-Hodge operators on compact manifolds with boundary. We give two kinds of operator-theoretic explanations of the gravitational action in the case of four dimensional compact manifolds with flat boundary.