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The van der Waals interaction
1.See, e.g., E. Merzbacher, Quantum Mechanics (Wiley, New York, 1998).
2.H. Margenau and N. R. Kestner, Theory of Intermolecular Forces (Pergamon, New York, 1969).
3.See, e.g., D. Park, Introduction to the Quantum Theory (McGraw–Hill, New York, 1974),
3.Chap. 16.4. See, especially, P. W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic, New York, 1994);
3.E. A. Power, Introductory Quantum Electrodynamics (Longmans, London, 1964).
4.This interaction between two polarizable systems is sometimes called the “dispersive” van der Waals force, since it is associated with the atomic polarizabilities which determine the index of refraction. This is related to, but distinct from, the “orientation” van der Waals interaction between two systems both of which have a permanent dipole moment and the “inductive” interaction between a polarizable and a polarized system.
5.C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw–Hill, New York, 1980).
6.H. Fujii and D. Kharzeev, “Long-range Forces of QCD,” Phys. Rev. D 60, 114039, 1–12 (1999). In this case the authors show that the long distance component of the interaction (which is the QCD analog of the van der Waals interaction in atomic physics) is due to the exchange of a pair of pions and leads to an interaction of the form
7.F. London, “Zur Theorie und Systematik der Molekularkräfte,” Z. Phys. 63, 245–279 (1930).
8.H. B. G. Casimir and D. Polder, “The Influence of Retardation on the London–van der Waals Force,” Phys. Rev. 73, 366–372 (1948).
9.C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1996), Chap. 3.
10.See, e.g., Ref. 1, Chap. 18.
11.C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley, New York, 1977), Chap. XI.
12.See, e.g., B. R. Holstein, Topics in Advanced Quantum Mechanics (Addison–Wesley, Reading, MA, 1992), Chap. 3.
13.E. A. Power and S. Zienau, “On the Radiation Contribution to the van der Waals Force,” Nuovo Cimento 6, 7–17 (1957).
14.D. Kaplan (private communication).
15.G. Feinberg and J. Sucher, “General Theory of the van der Waals Interaction: A Model-independent Approach,” Phys. Rev. A 2, 2395–2415 (1970).
16.In the forward direction this is simply the familiar optical theorem.
17.See, e.g., B. R. Holstein, “Electromagnetic Polarizability of the Nucleon,” Comments Nucl. Part. Phys. 20, 301–324 (1992).
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