Casimir Physics beyond the Proximity Force Approximation: The Derivative Expansion

We review the derivative expansion (DE) method in Casimir physics, an approach which extends the proximity force approximation (PFA). After introducing and motivating the DE in contexts other than the Casimir effect, we present different examples which correspond to that realm. We focus on different...

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Bibliographic Details
Published inPhysics (Online) Vol. 6; no. 1; pp. 290 - 316
Main Authors Fosco, César D., Lombardo, Fernando C., Mazzitelli, Francisco D.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.03.2024
Subjects
Accuracy
Approximation
Boundary conditions
Casimir effect
Casimir–Polder force
derivative expansion
Geometry
Hypotheses
Mathematical analysis
Nuclear physics
proximity force approximation
Quantum field theory
Quantum theory
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Summary:We review the derivative expansion (DE) method in Casimir physics, an approach which extends the proximity force approximation (PFA). After introducing and motivating the DE in contexts other than the Casimir effect, we present different examples which correspond to that realm. We focus on different particular geometries, boundary conditions, types of fields, and quantum and thermal fluctuations. Besides providing various examples where the method can be applied, we discuss a concrete example for which the DE cannot be applied; namely, the case of perfect Neumann conditions in 2+1 dimensions. By the same example, we show how a more realistic type of boundary condition circumvents the problem. We also comment on the application of the DE to the Casimir–Polder interaction which provides a broader perspective on particle–surface interactions.
ISSN:2624-8174
2624-8174
DOI:10.3390/physics6010020