Bordag, M.; Nikolaev, V. Beyond proximity force approximation in the Casimir effect. (English) Zbl 1170.81405 Int. J. Mod. Phys. A 24, No. 8-9, 1743-1747 (2009). Summary: We compare the analytical and numerical results for the Casimir force for the configuration of a plane and a cylinder in front of a plane. While for Dirichlet boundary conditions on both, plane and sphere or cylinder, agreement is found, for Neumann boundary conditions on either the plane or one of the two, cylinder or sphere, disagreement is found. This holds, for a sphere, also for different boundary conditions on the interacting surfaces. From recent, new numerical results for the cylinder, a general appearance of logarithmic contributions beyond PFA can be predicted. Cited in 1 Document MSC: 81T05 Axiomatic quantum field theory; operator algebras 81T99 Quantum field theory; related classical field theories 80A10 Classical and relativistic thermodynamics Keywords:Casimir effect; proximity force approximation PDFBibTeX XMLCite \textit{M. Bordag} and \textit{V. Nikolaev}, Int. J. Mod. Phys. A 24, No. 8--9, 1743--1747 (2009; Zbl 1170.81405) Full Text: DOI References: [1] DOI: 10.1088/1751-8113/41/16/164054 [2] DOI: 10.1103/PhysRevLett.98.050403 [3] DOI: 10.1007/BF01433225 [4] DOI: 10.1088/0305-4470/39/21/S14 [5] Gies H., JHEP 06 pp 018– [6] DOI: 10.1103/PhysRevD.73.025007 [7] DOI: 10.1103/PhysRevLett.96.080403 [8] DOI: 10.1103/PhysRevD.73.125018 [9] DOI: 10.1103/PhysRevD.74.045002 [10] Bordag M., J. Phys. A: Math. Theor. 41 pp 164001– [11] Emig T., J. Stat. Mech. 08 pp P04007– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.