Transformation operators and the Kastler-Kalau-Walze type theorems on 4-dimensional manifolds

TL;DR

This paper computes the lower-dimensional volume related to transformation operators on 4-dimensional spin manifolds with boundary and establishes a Kastler-Kalau-Walze type theorem for these operators on such manifolds.

Contribution

It introduces new computations of lower-dimensional volumes and extends the Kastler-Kalau-Walze theorem to transformation operators on 4-dimensional manifolds with boundary.

Findings

Computed the lower-dimensional volume Vol(1,1) for transformation operators.

Established a Kastler-Kalau-Walze type theorem for transformation operators.

Extended geometric analysis to 4-dimensional manifolds with boundary.

Abstract

In this paper, we compute the lower-dimensional volume Vol(1,1) about transformation operators for 4- dimensional spin manifolds with boundary and we also get the Kastler-Kalau-Walze type theorem about transformation operators on 4-dimensional compact manifolds with boundary.