Relative trace formulas for obstacle scattering with Neumann and transmission boundary conditions
Mathematical Physics
2026-05-21 v1 Analysis of PDEs
math.MP
Spectral Theory
Abstract
We consider the case of scattering by several obstacles in for . We establish a relative trace formula for Neumann and transmission boundary conditions analogous to the one obtained in arXiv:2002.07291 for Dirichlet boundary conditions. In the case of the trace has the interpretation of the Casimir energy of the obstacle configuration. In the one-dimensional case, we recover a rigorous version of the Lifshitz formula for the Casimir energy of parallel plates with frequency-independent electric permittivity and magnetic permeability. We thereby strengthen the mathematical foundations of the Casimir effect and demonstrate the flexibility of the rigorous approach established in arXiv:2104.09763 and arXiv:2002.07291.
Keywords
Cite
@article{arxiv.2605.21201,
title = {Relative trace formulas for obstacle scattering with Neumann and transmission boundary conditions},
author = {Arne Hofmann and Alexander Strohmaier},
journal= {arXiv preprint arXiv:2605.21201},
year = {2026}
}
Comments
50 pages