Infinity-free semiclassical evaluation of Casimir effects

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 58, Issue 2, 1998, Pages 935-953

  Schaden, Martin ^a   Spruch, Larry ^a,b  

^a POLYTECHNIC UNIVERSITY   (United States)

^b MAX PLANCK INSTITUT FÜR KERNPHYSIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4143143892     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.58.935     Document Type: Article

References (36)

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2. Three dielectric walls were first studied by I.E. Dzyaloshinskii, E.M. Lifshitz, and l. Pitaevskii, Adv. Phys. 10, 165 (1961). ADPHAH
3. The generalized argument theorem, first introduced in this area by N.G. van Kampen, B.R.A. Nijboer, and K. Schramm, Phys. Lett. 26A, 307 (1968), greatly simplifies the discussion. See also Ref. 2 for a nice review of the material.PYLAAG
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24. See, for example, L.E. Reichl, The Transition to Chaos (Springer, New York, 1992), Chap. 8 and references therein.
25. The semiclassical approximation to a Green function is accurate at least to order (Formula presented). For a photon in free space the semiclassical approximation to (Formula presented) and to (Formula presented) happens to be exact, but it is accurate only to first order in (Formula presented) for (Formula presented). The saddle-point approximation to the Laplace transform of (Formula presented) is exact only for (Formula presented), since it is proportional to a (Formula presented) function, i.e., a Gaussian of arbitrarily small width.
26. Note that, not surprisingly, Eq. (2.18) has a one-dimensional form. On setting (Formula presented) the perpendicular components in Eq. (2.16) drop out but, because of reflections (or images), the (Formula presented) components do not. Integration over (Formula presented) is therefore trivial.
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32. L. Spruch and Y. Tikochinsky, Phys. Rev. A 48, 4213 (1993) use a slightly differet approach. PLRAANSee also P.W. Milonni and M.-L. Shih, Contemporary Physics, edited by J.S. Dougdale (Taylor and Francis, London, 1993).
33. We also note that a number of results for the leading term of the forces between pairs of systems of various geometries have been obtained by J. Blocki, J. Randrup, W.J. Swiatecki, and C.F. Tang, Ann. Phys. (N.Y.) 105, 427 (1977). The approach used was somewhat similar to that used by Derjaguin 8.APNYA6
34. M. Schaden and L. Spruch (unpublished).
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