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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.04107 |
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| _version_ | 1866913224984625152 |
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| author | Dowker, J. S. |
| author_facet | Dowker, J. S. |
| contents | The contribution, E, of hyperbolic elements to the scalar Casimir energy on a compact quotient of the upper half hyperbolic plane is computed for a propagation operator conformal in three dimensions. Due to the proliferation of prime closed geodesics, the series form for the Casimir energy has an IR divergence. The expression for E is given as a sum of polylogarithms which allows the divergence to be isolated and rendered finite by an {\it ad hoc} Ramanujan renormalisation. The remaining part of E is computed using the specific lower length spectrum of the (2,3,7) triangle and a universal asymptotic form for larger lengths. The tentative value of E found is such as to make the total conformal Casimir energy on the triangle probably negative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04107 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Casimir energy of hyperbolic elements Dowker, J. S. High Energy Physics - Theory Spectral Theory The contribution, E, of hyperbolic elements to the scalar Casimir energy on a compact quotient of the upper half hyperbolic plane is computed for a propagation operator conformal in three dimensions. Due to the proliferation of prime closed geodesics, the series form for the Casimir energy has an IR divergence. The expression for E is given as a sum of polylogarithms which allows the divergence to be isolated and rendered finite by an {\it ad hoc} Ramanujan renormalisation. The remaining part of E is computed using the specific lower length spectrum of the (2,3,7) triangle and a universal asymptotic form for larger lengths. The tentative value of E found is such as to make the total conformal Casimir energy on the triangle probably negative. |
| title | Casimir energy of hyperbolic elements |
| topic | High Energy Physics - Theory Spectral Theory |
| url | https://arxiv.org/abs/2402.04107 |