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Comment on “On the role of dissipation on the Casimir-Polder potential between molecules in dielectric media” [J. Chem. Phys.133, 164501 (2010)]
1. I. E. Dzyaloshinskii and L. P. Pitaevskii, Sov. Phys. JETP 9, 1282 (1959).
1.See also L. P. Pitaevskii, “On the problem of van der Waals forces in dielectric media,” in Casimir Physics, Lecture Notes in Physics, edited by D. A. R. Dalvit, P. W. Milonni, D. C. Roberts, and F. S. S. Rosa (Springer-Verlag, Berlin, 2011);
4.We consider here only electrically polarizable guest atoms and host media.
7.Analyticity of the Green function in I+ follows from the same (Kramers-Kronig) causality arguments that demand that the dielectric permittivity and the refractive index have this property. See, for instance, J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 309.
7.In the case of the dyadic Green function for a dielectric medium, analyticity in I+ has been emphasized by other authors. See, for instance, A. Narayanaswamy and G. Chen, J. Quant. Spectrosc. Radiat. Transf. 111, 1877 (2010).
8.A simple example: , β > 0, is analytic in I+, but Im[ is not.
9.See, for instance, P. W. Milonni, The Quantum Vacuum. An Introduction to Quantum Electrodynamics (Academic, San Diego, 1994), Sec. 4.6, and references therein.
9.The nonretarded part of the transverse Green function is cancelled by the longitudinal Green function, so that the complete Green function is properly retarded. These properties of the Green function used in Ref. 2 in the case of an absorbing medium can be seen explicitly in Appendix A of S. M. Barnett, B. Huttner, R. Loudon, and R. Matloob, J. Phys. B 29, 3763 (1996).
10.For an interesting discussion of this point, and its implications for retardation, see J. D. Jackson, Eur. J. Phys. 31, L79 (2010), where it is remarked that “The longitudinal and transverse components [of the electric field] have no separate physical realities; only the sum is physical.”
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J. J. Rodriguez and A. Salam [J. Chem. Phys.133, 164501 (2010)]10.1063/1.3495954 find discrepancies between their calculation and a previously published one [S. Spagnolo, D. A. R. Dalvit, and P. W. Milonni, Phys. Rev. A75, 052117 (2007)]10.1103/PhysRevA.75.052117 for the van der Waals interaction of two guest molecules in a host dielectric medium. We trace these discrepancies to what we regard as fundamental errors in the calculation by Rodriguez and Salam.
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