2016/07/11 by Giuseppe Bimonte
Mathematics · Physics and Astronomy · #Casimir effect #Casimir pressure #Classical mechanics #Conformal map #Cosmology and Gravitation Theories #Euclidean geometry #Geometry #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Order (exchange) #Physics #Quantum Electrodynamics and Casimir Effect #RADIUS #SPHERES #Simple (philosophy) #Symmetry (geometry) #quant-ph
paper · pdf · doi:10.1103/physrevd.94.085021
published as Phys. ReV. D 94, 085021 (2016) · 19 pages, 2 figures
arxiv created 2016/07/11 · openalex created_date 2016/08/23 · openalex publication_date 2016/10/21 · arxiv updated 2016/10/24 · openalex updated_date 2026/08/05
Exploiting conformal symmetry, we derive a simple exact formula for the classical electromagnetic Casimir interaction of two perfectly conducting three-spheres, including the sphere-plate geometry as a special case, in four Euclidean dimensions. We verify that the short distance expansion of the Casimir energy agrees to leading order with the proximity force approximation (PFA), while the next-to-leading order is in agreement with a recently proposed derivative expansion of the Casimir energy. At the next-to-next-to-leading order we find a nonanalytic correction to PFA, which for a sphere-plate system is of the order of (d/R)3/2log(d/R), where d is the separation and R the sphere radius.