Dimensional reduction formulae for spectral traces and Casimir energies
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909150733139968 |
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| author | Strohmaier, Alexander |
| author_facet | Strohmaier, Alexander |
| contents | This short letter considers the case of acoustic scattering by several obstacles in $\mathbb{R}^{d+r}$ for $r,d \geq 1$ of the form $Ω\times \mathbb{R}^r$, where $Ω$ is a smooth bounded domain in $\mathbb{R}^d$. As a main result a von-Neumann-trace formula for the relative trace is obtained in this setting. As a special case we obtain a dimensional reduction formula for the Casimir energy for the massive and massless scalar fields in this configuration $Ω\times \mathbb{R}^r$ per unit volume in $\mathbb{R}^r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dimensional reduction formulae for spectral traces and Casimir energies Strohmaier, Alexander Mathematical Physics Analysis of PDEs 81T55, 11F72 This short letter considers the case of acoustic scattering by several obstacles in $\mathbb{R}^{d+r}$ for $r,d \geq 1$ of the form $Ω\times \mathbb{R}^r$, where $Ω$ is a smooth bounded domain in $\mathbb{R}^d$. As a main result a von-Neumann-trace formula for the relative trace is obtained in this setting. As a special case we obtain a dimensional reduction formula for the Casimir energy for the massive and massless scalar fields in this configuration $Ω\times \mathbb{R}^r$ per unit volume in $\mathbb{R}^r$. |
| title | Dimensional reduction formulae for spectral traces and Casimir energies |
| topic | Mathematical Physics Analysis of PDEs 81T55, 11F72 |
| url | https://arxiv.org/abs/2402.16738 |