# The Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary

## Abstract

In this paper, we define lower dimensional volumes of spin manifolds with boundary. We compute the lower dimensional volume V ol{sub 6}{sup (1,3)} for 6-dimensional spin manifolds with boundary and derive the gravity on boundary from the noncommutative residue associated with Dirac operators. For 6-dimensional manifolds with boundary, we also get a Kastler-Kalau-Walze type theorem for a general fourth order operator.

- Authors:

- School of Science, Tianjin University of Technology and Education, Tianjin 300222 (China)
- School of Mathematics and Statistics, Northeast Normal University, Changchun 130024 (China)

- Publication Date:

- OSTI Identifier:
- 22403145

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 56; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMMUTATION RELATIONS; DIRAC OPERATORS; GRAVITATION; QUANTUM ELECTRODYNAMICS; SPIN

### Citation Formats

```
Wang, Jian, and Wang, Yong, E-mail: wangj484@nenu.edu.cn, E-mail: wangy581@nenu.edu.cn.
```*The Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary*. United States: N. p., 2015.
Web. doi:10.1063/1.4919889.

```
Wang, Jian, & Wang, Yong, E-mail: wangj484@nenu.edu.cn, E-mail: wangy581@nenu.edu.cn.
```*The Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary*. United States. doi:10.1063/1.4919889.

```
Wang, Jian, and Wang, Yong, E-mail: wangj484@nenu.edu.cn, E-mail: wangy581@nenu.edu.cn. Fri .
"The Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary". United States. doi:10.1063/1.4919889.
```

```
@article{osti_22403145,
```

title = {The Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary},

author = {Wang, Jian and Wang, Yong, E-mail: wangj484@nenu.edu.cn, E-mail: wangy581@nenu.edu.cn},

abstractNote = {In this paper, we define lower dimensional volumes of spin manifolds with boundary. We compute the lower dimensional volume V ol{sub 6}{sup (1,3)} for 6-dimensional spin manifolds with boundary and derive the gravity on boundary from the noncommutative residue associated with Dirac operators. For 6-dimensional manifolds with boundary, we also get a Kastler-Kalau-Walze type theorem for a general fourth order operator.},

doi = {10.1063/1.4919889},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 5,

volume = 56,

place = {United States},

year = {2015},

month = {5}

}

DOI: 10.1063/1.4919889

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.