On the corrections beyond proximity force approximation (PFA)

Abstract

We recalculate the first analytic correction beyond PFA for a sphere in front of a plane for a scalar field and for the electromagnetic field. We use the method of Bordag and Nikolaev [J.Phys.A, {\bf 41} (2008) p.164002]. We confirm their result for Dirichlet boundary conditions whereas we find a different one for Robin, Neumann and conductor boundary conditions. The difference can be traced back to a sign error. As a result, the corrections depend on the Robin parameter. Agreement is found with a very recent method of derivative expansion.

9 pages. Some changes in the conclusion

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• The Casimir effect for a sphere and a cylinder in front of plane and corrections to the proximity force theorem
• Worldline algorithms for Casimir configurations
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• The proximity force approximation for the Casimir energy as a derivative expansion
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