The noncommutative residue about Witten deformation
type: Item
instance of: scholarly article
title: The noncommutative residue about Witten deformation
zbMATH Open document ID: 1414.58017
author: Kai Hua Bao
author: Ai Hui Sun
author: Chao Deng
publication date: 2019-03-27T00:00:00Z
review text: From the introduction: ``The motivation of this paper is to give two kinds of operator theoretic explanation of the gravitational action for manifolds with boundary by the noncommutative residue associated with the Witten deformation, and prove two Kastler-Kalau-Walze type theorems for manifolds with boundary. \par This paper is organized as follows: In Section 2, we recall the definition of Witten deformation $D_T$. In Section 3, we recall the definition of lower dimensional volumes of spin manifolds with boundary. In Section 4, we compute the lower dimensional volume $Vol_{4}^{(1,1)}$ and get a Kastler-Kalau-Walze type theorem in this case. We also give a theoretic explanation of the gravitational action for 4-dimensional manifolds with boundary by this noncommutative residue. In Section 5, we compute the lower dimensional volume $Vol_{6}^{(2,2)}$ and get a Kastler-Kalau-Walze type theorem in this case. We also give a theoretic explanation of the gravitational action for 6-dimensional manifolds with boundary by this noncommutative residue.'' \par The authors also explain in the introduction that the Kastler-Kalau-Walze theorem states the observation of of A. Connes, that the noncommutative residue of the inverse of the Dirac operator is proportional to the Hilbert-Einstein action.
reviewed by: Iakovos Androulidakis
Mathematics Subject Classification ID: 58J42
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 46L87
zbMATH DE Number: 7043622
zbMATH Keywords: lower-dimensional volumes
zbMATH Keywords: noncommutative residue
zbMATH Keywords: gravitational action
zbMATH Keywords: Witten deformation
MaRDI profile type: Publication
full work available at URL: s10114-018-8069-7
OpenAlex ID: W2908975249
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Wikidata QID: Q128592875
DOI: 10.1007/S10114-018-8069-7
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 7043622