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arXiv · 2402.16738

Dimensional reduction formulae for spectral traces and Casimir energies

Alexander Strohmaier
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Abstract

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 $\Omega \times \mathbb{R}^r$, where $\Omega$ 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 $\Omega \times \mathbb{R}^r$ per unit volume in $\mathbb{R}^r$.

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Alexander Strohmaier. 2024-02-26. Dimensional reduction formulae for spectral traces and Casimir energies. https://arxiv.org/abs/2402.16738

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