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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.18038 |
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| _version_ | 1866916805889490944 |
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| author | Wang, Jian Wang, Yong |
| author_facet | Wang, Jian Wang, Yong |
| contents | In this paper, a simple proof of the divergence theorem is given by using the Dirac operator and noncommutative residues. Then we extend the divergence theorem to compact manifolds with boundary by the noncommutative residue of the B-algebra. Furthermore, we present some spectral geometric functionals which we call spectral divergence functionals, and we calculate the spectral divergence functionals of manifolds with (or without) boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The noncommutative residue, divergence theorems and the spectral geometry functional Wang, Jian Wang, Yong Mathematical Physics In this paper, a simple proof of the divergence theorem is given by using the Dirac operator and noncommutative residues. Then we extend the divergence theorem to compact manifolds with boundary by the noncommutative residue of the B-algebra. Furthermore, we present some spectral geometric functionals which we call spectral divergence functionals, and we calculate the spectral divergence functionals of manifolds with (or without) boundary. |
| title | The noncommutative residue, divergence theorems and the spectral geometry functional |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2506.18038 |