The spectral torsion for the rescaled Dirac operator

TL;DR

This paper explores the spectral torsion of rescaled Dirac operators on compact spin manifolds, providing explicit examples and computations based on Clifford multiplication and differential forms.

Contribution

It introduces four new examples of rescaled Dirac operators and computes their spectral torsion using Clifford algebra techniques.

Findings

Explicit spectral torsion formulas for four rescaled Dirac operators

Demonstration of the impact of perturbations on spectral properties

Application of Clifford multiplication in spectral analysis

Abstract

In the paper, we give four different examples of the rescaled Dirac operator by the perturbation of the function f. Further, based on the trilinear Clifford multiplication by functional of differential one-forms, we compute the spectral torsion for four kinds of rescaled Dirac operator on even-dimensional oriented compact spin Riemannian manifolds without boundary.