Details
| Original language | English |
|---|---|
| Article number | 66 |
| Number of pages | 9 |
| Journal | Letters in mathematical physics |
| Volume | 114 |
| Issue number | 3 |
| Publication status | Published - 24 May 2024 |
Abstract
This short letter considers the case of acoustic scattering by several obstacles in Rd+r for r,d≥1 of the form Ω×Rr, where Ω is a smooth bounded domain in Rd. 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×Rr per unit volume in Rr.
Keywords
- Casimir effect, Obstacle scattering, Trace formula
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
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In: Letters in mathematical physics, Vol. 114, No. 3, 66, 24.05.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Dimensional reduction formulae for spectral traces and Casimir energies
AU - Strohmaier, Alexander
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2024/5/24
Y1 - 2024/5/24
N2 - This short letter considers the case of acoustic scattering by several obstacles in Rd+r for r,d≥1 of the form Ω×Rr, where Ω is a smooth bounded domain in Rd. 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×Rr per unit volume in Rr.
AB - This short letter considers the case of acoustic scattering by several obstacles in Rd+r for r,d≥1 of the form Ω×Rr, where Ω is a smooth bounded domain in Rd. 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×Rr per unit volume in Rr.
KW - Casimir effect
KW - Obstacle scattering
KW - Trace formula
UR - http://www.scopus.com/inward/record.url?scp=85194531162&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2402.16738
DO - 10.48550/arXiv.2402.16738
M3 - Article
AN - SCOPUS:85194531162
VL - 114
JO - Letters in mathematical physics
JF - Letters in mathematical physics
SN - 0377-9017
IS - 3
M1 - 66
ER -