The spectral torsion for the one form rescaled Dirac operator

TL;DR

This paper introduces an extended spectral torsion concept related to Dirac operators, specifically computing it for the one form rescaled Dirac operator on even-dimensional spin manifolds, advancing spectral geometry understanding.

Contribution

It presents a new form of spectral torsion extending previous definitions and computes it explicitly for a specific rescaled Dirac operator on even-dimensional spin manifolds.

Findings

Extended spectral torsion definition for Dirac operators.

Explicit computation of spectral torsion for the one form rescaled Dirac operator.

Application to even-dimensional spin manifolds without boundary.

Abstract

The spectral torsion is defined by three vector fields and Dirac operators and the noncommutative residue. Motivated by the spectral torsion and the one form rescaled Dirac operator, we give some new spectral torsion which is the extension of spectral torsion for Dirac operators, and compute the spectral torsion for the one form rescaled Dirac operator on even-dimensional spin manifolds without boundary.