Topological aspects of zero modes in cavity resonators
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914276643438592 |
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| author | Kamigaito, Osamu |
| author_facet | Kamigaito, Osamu |
| contents | We discuss the relationship between the zero modes of electromagnetic fields in a cavity resonator and the cavity's topological characteristics. We show that the dimension of the electromagnetic zero-mode space coincides with the dimension of the corresponding homology group of the cavity. Moreover, we prove that the alternating sum of the dimensions of the electromagnetic zero-mode spaces is closely related to the Euler characteristic of the cavity boundary, and hence to the integral of the curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11989 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological aspects of zero modes in cavity resonators Kamigaito, Osamu Accelerator Physics Classical Physics We discuss the relationship between the zero modes of electromagnetic fields in a cavity resonator and the cavity's topological characteristics. We show that the dimension of the electromagnetic zero-mode space coincides with the dimension of the corresponding homology group of the cavity. Moreover, we prove that the alternating sum of the dimensions of the electromagnetic zero-mode spaces is closely related to the Euler characteristic of the cavity boundary, and hence to the integral of the curvature. |
| title | Topological aspects of zero modes in cavity resonators |
| topic | Accelerator Physics Classical Physics |
| url | https://arxiv.org/abs/2601.11989 |