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Introduction

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Part of the book series: Lecture Notes in Physics ((LNP,volume 834))

Abstract

Casimir forces are associated with topological constraints on quantum fields. The most famous such effect was predicted in 1948 by Casimir, who found that there is an attractive force

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References

  1. Casimir, H.B.G.: On the attraction between two perfectly conducting plates. Proc. K. Ned. Akad. Wet. 51, 793 (1948)

    MATH  Google Scholar 

  2. Lifshitz, E.M.: The theory of molecular attractive forces between solids. Sov. Phys. JETP 2, 73 (1956)

    MathSciNet  Google Scholar 

  3. London, F.: Theory and system of molecular forces. Z. Phys. 63, 245 (1930)

    Article  ADS  MATH  Google Scholar 

  4. See, for instance, V. A. Parsegian, Van der Waals Forces: A Handbook for Biologists, Chemists, Engineers, and Physicists (Cambridge University Press, N. Y., 2006).

    Google Scholar 

  5. Verwey, E.J.W., Overbeek, J.T.G.: Theory of the Stability of Lyophobic Colloids. Elsevier, Amsterdam (1948)

    Google Scholar 

  6. Casimir, H.B.G., Polder, D.: The influence of retardation on the London-van der Waals forces. Phys. Rev. 73, 360 (1948)

    Article  ADS  MATH  Google Scholar 

  7. Langmuir, I.: Role of attractive and repulsive forces in formation of tactoids, thixotropic gels, protein crystals and coacervates. J. Chem. Phys. 6, 873 (1938)

    Article  ADS  Google Scholar 

  8. Casimir, H.B.G.: Communication to P.W. Milonni, 12 March (1992)

    Google Scholar 

  9. Some of Einstein’s work related to zero-point energy is reviewed in P.W. Milonni, The Quantum Vacuum. An Introduction to Quantum Electrodynamics (Academic, San Diego, 1994).

    Google Scholar 

  10. Gearhart, C.A.: ‘Astonishing successes’ and ‘bitter disappointment’: The specific heat of hydrogen in quantum theory. Arch. Hist. Exact Sci. 64, 113 (2010)

    Article  Google Scholar 

  11. Mulliken, R.S.: The band spectrum of boron monoxide. Nature 114, 349 (1924)

    Article  ADS  Google Scholar 

  12. Stenger, J., Inouye, S., Chikkatur, A.P., Stamper-Kurn, D.M., Pritchard, D.E., Ketterle, W.: Bragg spectroscopy of a Bose-Einstein condensate. Phys. Rev. Lett. 82, 4569 (1999)

    Article  ADS  Google Scholar 

  13. See, for instance, Milonni, P.W., Schaden, M., Spruch, L.: The Lamb shift of an atom in a dielectric medium. Phys. Rev. A 59, 4259 (1999) and references therein

    Google Scholar 

  14. See, for example, Reference [9] and references therein

    Google Scholar 

  15. Spruch, L.L., Kelsey, E.J.: Vacuum fluctuation and retardation effects in long-range potentials. Phys. Rev. A. 18, 845 (1978)

    Article  ADS  Google Scholar 

  16. Feinberg, G., Sucher, J.J., Au, C.K.: The dispersion theory of dispersion forces. Phys. Rep. 180, 83 (1978)

    Article  ADS  Google Scholar 

  17. Itzykson, C., Zuber, J.-B.: Quantum Field Theory, pp. 141. McGraw-Hill, N.Y. (1980)

    Google Scholar 

  18. Rosa, F.S.S., Dalvit, D.A.R., Milonni, P.W.: Electromagnetic energy, absorption, and Casimir forces: Uniform dielectric media in thermal equilibrium. Phys. Rev. A. 81, 033812 (2010)

    Article  ADS  Google Scholar 

  19. Rosa, F.S.S., Dalvit, D.A.R., Milonni, P.W.: to be submitted for publication. Expressions equivalent to (37) but with different choices for the definition of the Green dyadic may be found, for instance, in T. Gruner and D.-G. Welsch, Green-function approach to the radiation-field quantization for homogeneous and inhomogeneous Kramers-Kronig dielectrics. Phys. Rev. A 53, 1818 (1996) and M.S. Tomas, Casimir force in absorbing monolayers. Phys. Rev. A 66, 052103 (2002)

    Google Scholar 

  20. Dzyaloshinskii, I.E., Pitaevskii, L.P.: Van der Waals forces in an inhomogeneous dielectric. Sov. Phys. JETP 9, 1282 (1959)

    Google Scholar 

  21. Dzyaloshinskii, I.E., Lifshitz, E.M., Pitaevskii, L.P.: The general theory of van der Waals forces. Adv. Phys. 10, 165 (1961)

    Article  MathSciNet  ADS  Google Scholar 

  22. See also A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (Dover, N.Y., 1975)

    Google Scholar 

  23. Schwinger, J., DeRaad, L.L. Jr., Milton, K.A.: Casimir effect in dielectrics. Ann. Phys. (N.Y.) 115, 1 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  24. Axilrod, B.M., Teller, E.: Interaction of the van der Waals type between three atoms. J.Chem. Phys. 11, 299 (1943)

    Article  ADS  Google Scholar 

  25. van Kampen, N.G., Nijboer, B.R.A., Schram, K.: On the macroscopic theory of van der Waals forces. Phys. Lett. 26, 307 (1968)

    Article  Google Scholar 

  26. See, for instance, Reference [9], Sect. 8.3.

    Google Scholar 

  27. Sabisky, E.S., Anderson, C.H.: Verification of the Lifshitz theory of the van der Waals potential using liquid-helium films. Phys. Rev. A 7, 790 (1973)

    Article  ADS  Google Scholar 

  28. Kats, E.I.: Influence of nonlocality effects on van der Waals interaction. Sov. Phys. JETP 46, 109 (1977)

    ADS  Google Scholar 

  29. For a detailed review of the scattering approach see, for instance, the chapters by A. Lambrecht et al and S.J. Rahi et al in this volume

    Google Scholar 

  30. Derjaguin, B.V., Rabinovich, Y.I., Churaev, N.V.: Direct measurement of molecular forces. Nature 272, 313 (1978) and references therein to related work of Derjaguin et al

    Google Scholar 

  31. It should be noted that Bressi et al managed to measure with about 15% precision the Casimir force between (nearly) parallel metallic plates: G. Bressi, G. Carugno, R. Onofrio, and G. Ruoso, “Measurement of the Casimir force between parallel metallic surfaces," Phys. Rev. Lett. 88, 041804 (2002)

    Google Scholar 

  32. Krause, D.E., Decca, R.S., López, D., Fischbach, E.: Experimental investigation of the Casimir force beyond the proximity-force approximation. Phys. Rev. Lett. 98, 050403 (2007)

    Article  ADS  Google Scholar 

  33. Sparnaay, M.J.: The historical background of the Casimir effect. In: Sarlemijn, A., Sparnaay, M.J. (eds) Physics in the Making, Elsevier, Amsterdam (1989)

    Google Scholar 

  34. Sparnaay, M.J.: Attractive forces between flat plates. Nature 180, 334 (1957)

    Article  ADS  Google Scholar 

  35. Sparnaay, M.J: Measurements of attractive forces between flat plates. Physica 24, 751 (1958)

    Article  ADS  Google Scholar 

  36. Lamoreaux, S.: Demonstration of the Casimir force in the 0.6 to 6 \(\mu \,\hbox{m}\) range. Phys. Rev. Lett. 78, 5 (1997)

    Article  ADS  Google Scholar 

  37. See also S. Lamoreaux, The Casimir force: background, experiments, and applications. Rep. Prog. Phys. 68, 201 (2005) and “Casimir forces: Still surprising after 60 years," Physics Today (February, 2007), 40-45

    Google Scholar 

  38. Mohideen, U., Roy, A.: Precision measurement of the Casimir force from 0.1 to 0.9 \(\mu \,\hbox{m}\). Phys. Rev. Lett. 81, 4549 (1998)

    Article  ADS  Google Scholar 

  39. See also M. Bordag, U. Mohideen, V.M. Mostepanenko, “New developments in the Casimir effect," Phys. Rep. 353, 1 (2001)

    Google Scholar 

  40. Bordag, M., Klimchitskaya, G.L., Mohideen, U., Mostepanenko, V.M.: Advances in the Casimir Effect. Oxford University Press, N.Y. (2009)

    Book  MATH  Google Scholar 

  41. Chan, H.B., Aksyuk, V.A., Kleiman, R.N., Bishop, D.J., Capasso, F.: Quantum mechanical actuation of microelectromechanical systems by the Casimir force. Science 291, 1941 (2001)

    Article  ADS  Google Scholar 

  42. Chan, H.B., Aksyuk, V.A., Kleiman, R.N., Bishop, D.J., Capasso, F.: Nonlinear micromechanical Casimir oscillator. Phys. Rev. Lett. 87, 211801 (2001)

    Article  ADS  Google Scholar 

  43. Decca, R.S., López, D., Fischbach, E., Krause, D.E.: Measurement of the Casimir force between dissimilar metals. Phys. Rev. Lett. 91, 504021 (2003)

    Article  Google Scholar 

  44. de Man, S., HeeckK. Wijngaarden, R.J., Iannuzzi, D.: Halving the Casimir force with conductive oxides. Phys. Rev. Lett. 103, 040402 (2009)

    Article  Google Scholar 

  45. de Man, S., Heeck, K., Smith, K., Wijngaarden, R.J., Iannuzzi, D.: Casimir force measurements in air: two birds with one stone. Int. J. Mod. Phys. A 25, 2231 (2010)

    Article  ADS  Google Scholar 

  46. Sukenik, C.I., Boshier, M.G., Cho, D., Sandoghar, V., Hinds, E.A.: Measurement of the Casimir-Polder force. Phys. Rev. Lett. 70, 560 (1993)

    Article  ADS  Google Scholar 

  47. See for instance A.A. Feiler, L. Bergstrom, M.W. Rutland, “Superlubricity using repulsive van der Waals forces," Langmuir 24, 2274 (2008), and references therein.

    Google Scholar 

  48. Munday, J.N., Capasso, F., Parsegian, V.A.: Measured long-range Casimir-Lifshitz forces. Nature 457, 170 (2009)

    Article  ADS  Google Scholar 

  49. Boyer, T.H.: Van der Waals forces and zero-point energy for dielectric and permeable materials. Phys. Rev. A 9, 2078 (1974)

    Article  ADS  Google Scholar 

  50. Feinberg, G., Sucher, J.: General theory of the van der Waals interaction: A model-independent approach. Phys. Rev. A 2, 2395 (1970)

    Article  ADS  Google Scholar 

  51. Rosa, F.S.S., Dalvit, D.A.R., Milonni, P.W.: Casimir-Lifshitz theory and metamaterials. Phys. Rev. Lett. 100, 183602 (2008); “Casimir interactions for anisotropic magnetodielectric metamaterials”, Phys. Rev. A 78, 032117 (2008)

    Google Scholar 

  52. Rahi, S.J., Kardar, M., Emig, T.: Constraints on stable equilibria with fluctuation-induced (Casimir) forces. Phys. Rev. Lett. 105, 070404 (2010)

    Article  ADS  Google Scholar 

  53. Boyer, T.H.: Quantum zero-point energy and long-range forces. Ann. Phys. (N.Y.) 56, 474 (1970)

    Article  ADS  Google Scholar 

  54. Schaden, M.: Semiclassical estimates of electromagnetic Casimir self-energies of spherical and cylindrical metallic shells. Phys. Rev. A 82, 022113 (2010)

    Article  ADS  Google Scholar 

  55. See, for instance, Reference [9] and references therein.

    Google Scholar 

  56. Jaffe, R.L.: Casimir effect and the quantum vacuum. Phys. Rev. D. 72, 021301(R) (2005)

    ADS  Google Scholar 

  57. Fisher, M.E., de Gennes, P.-G.: Wall phenomena in a critical binary mixture. C.R. Acad. Sci. Paris B. 287, 209 (1978)

    Google Scholar 

  58. Garcia, R., Chan, M.H.W.: Critical Casimir effect near the \(^3\hbox{He}\)-\(^4\hbox{He}\) tricritical point. Phys. Rev. Lett. 88, 086101 (1978)

    Article  ADS  Google Scholar 

  59. Hertlein, C., Helden, L., Gambassi, A., Dietrich, S., Bechinger, C.: Direct measurement of critical Casimir forces. Nature 451, 172 (2008)

    Article  ADS  Google Scholar 

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Dalvit, D.A.R., Milonni, P.W., Roberts, D.C., Rosa, F.S.S. (2011). Introduction. In: Dalvit, D., Milonni, P., Roberts, D., da Rosa, F. (eds) Casimir Physics. Lecture Notes in Physics, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20288-9_1

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  • DOI: https://doi.org/10.1007/978-3-642-20288-9_1

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