A Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator

TL;DR

This paper establishes a Kastler-Kalau-Walze type theorem for the J-twist Dirac operator on certain low-dimensional almost product Riemannian spin manifolds with boundary, extending geometric analysis tools.

Contribution

It introduces a Lichnerowicz type formula and proves a Kastler-Kalau-Walze theorem for the J-twist Dirac operator on 3D and 4D manifolds with boundary, a novel extension.

Findings

Derived a Lichnerowicz type formula for D_J.

Proved a Kastler-Kalau-Walze theorem for D_J on 3D and 4D manifolds.

Extended geometric analysis techniques to J-twist Dirac operators.

Abstract

In this paper, we give a Lichnerowicz type formula for the J-twist D_J of the Dirac operator. And we prove a Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator on 3-dimensional and 4-dimensional almost product Riemannian spin manifold with boundary.