Casimir Physics beyond the Proximity Force Approximation: The Derivative Expansion

Abstract

We review the derivative expansion (DE) method in Casimir physics, an approach whichextends the proximity force approximation (PFA). After introducing and motivating the DE in contextsother than the Casimir effect, we present different examples which correspond to that realm. We focuson different particular geometries, boundary conditions, types of fields, and quantum and thermalfluctuations. Besides providing various examples where the method can be applied, we discuss aconcrete example for which the DE cannot be applied; namely, the case of perfect Neumann conditionsin 2 + 1 dimensions. By the same example, we show how a more realistic type of boundary conditioncircumvents the problem. We also comment on the application of the DE to the Casimir–Polderinteraction which provides a broader perspective on particle–surface interactions.