The pseudo-differential perturbations of the Dirac operator and the Kastler-Kalau-Walze type theorems
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912044432752640 |
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| author | Wu, Tong Wang, Yong |
| author_facet | Wu, Tong Wang, Yong |
| contents | We define two types of pseudo-differential perturbations of the Dirac operator within the framework of the noncommutative geometry. And we obtain the noncommutative residue of the inverse square of these perturbations on 4-dimensional compact manifolds without boundary. As a generalization of the result of noncommutative residue on closed manifolds, we prove the Kastler-Kalau-Walze type theorems for these perturbations on 4-dimensional compact manifolds with boundary. Finally, several examples in which we can consider the corresponding pseudo-differential operators and the Kastler-Kalau-Walze type theorems are listed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The pseudo-differential perturbations of the Dirac operator and the Kastler-Kalau-Walze type theorems Wu, Tong Wang, Yong Differential Geometry We define two types of pseudo-differential perturbations of the Dirac operator within the framework of the noncommutative geometry. And we obtain the noncommutative residue of the inverse square of these perturbations on 4-dimensional compact manifolds without boundary. As a generalization of the result of noncommutative residue on closed manifolds, we prove the Kastler-Kalau-Walze type theorems for these perturbations on 4-dimensional compact manifolds with boundary. Finally, several examples in which we can consider the corresponding pseudo-differential operators and the Kastler-Kalau-Walze type theorems are listed. |
| title | The pseudo-differential perturbations of the Dirac operator and the Kastler-Kalau-Walze type theorems |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2401.10909 |