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.

41 pages, 2 figures, LaTeX, more details added, typos corrected, references added

References in corpus (6)

• Casimir forces between arbitrary compact objects
• Casimir forces in a T operator approach
• Casimir Forces between Compact Objects: I. The Scalar Case
• Multiple Scattering Methods in Casimir Calculations
• Casimir forces between arbitrary compact objects: Scalar and electromagnetic field
• Vacuum Energy as Spectral Geometry

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