A mathematical analysis of Casimir interactions I: The scalar field

Abstract

Starting from the construction of the free quantum scalar field of mass $m\ge 0$ we give mathematically precise and rigorous versions of three different approaches to computing the Casimir forces between compact obstacles. We then prove that they are equivalent.

arXiv comment41 pages, 2 figures, LaTeX, more details added, typos corrected, references added

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Cited by in corpus (4)

• The classical and quantum photon field for non-compact manifolds with boundary and in possibly inhomogeneous media
• A note on "Algebraic approach to Casimir force between two $\delta$-like potentials" (K. Ziemian, Ann. Henri Poincaré, Online First, 2021)
• The relative trace formula in electromagnetic scattering and boundary layer operators
• Trace singularities in obstacle scattering and the Poisson relation for the relative trace