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International Journal of Theoretical Physics

, Volume 54, Issue 8, pp 2623–2631 | Cite as

The Proximity Force Approximation for the Casimir Energy of Plate-Sphere and Sphere-Sphere Systems in the Presence of One Extra Compactified Universal Dimension

  • Hongbo Cheng
Article
  • 56 Downloads

Abstract

The Casimir energies for plate-sphere system and sphere-sphere systems under PFA in the presence of one extra compactified universal dimension are analyzed. We find that the Casimir energy between a plate and a sphere in the case of sphere-based PFA is divergent. The Casimir energy of plate-sphere system in the case of plate-based PFA is finite and keeps negative. The extra-dimension corrections to the Casimir energy will be more manifest if the sphere is larger or farther away from the plate. It is shown that the negative Casimir energy for two spheres is also associated with the sizes of spheres and extra space. The larger spheres and the longer distance between them make the influence from the additional dimension stronger.

Keywords

Casimir energy Kaluza-Klein model 

Notes

Acknowledgments

The author thanks Professor K. Milton and Professor M. Bordag for helpful discussions. This work is supported by NSFC No. 10875043 and is partly supported by the Shanghai Research Foundation No. 07dz22020.

References

  1. 1.
    Casimir, H.B.G.: Proc. Kon. Ned. Akad. Wetensch. 51, 793 (1948)MATHGoogle Scholar
  2. 2.
    Lamoreaux, S.K.: Phys. Rev. Lett. 78, 5 (1997)ADSCrossRefGoogle Scholar
  3. 3.
    Lamoreaux, S.K.: Phys. Rev. Lett. 81, 5475(E) (1998)ADSCrossRefGoogle Scholar
  4. 4.
    Mohideen, U., Roy, A.: Phys. Rev. Lett. 81, 4549 (1998)ADSCrossRefGoogle Scholar
  5. 5.
    Roy, A., et al.: Phys. Rev. D 60, 111101(R) (1999)ADSCrossRefGoogle Scholar
  6. 6.
    Chan, H.B., et al.: Science 291, 1941 (2001)ADSCrossRefGoogle Scholar
  7. 7.
    Bressi, G., Carugno, G., Onofrio, R., Ruoso, G.: Phys. Rev. Lett. 88, 041804 (2002)ADSCrossRefMATHGoogle Scholar
  8. 8.
    Chen, F., et al.: Phys. Rev. Lett. 88, 101801 (2002)ADSCrossRefGoogle Scholar
  9. 9.
    Bordag, M., Mohideen, U., Mostepanenko, V.M.: Phys. Rep. 353, 1 (2001)MathSciNetADSCrossRefMATHGoogle Scholar
  10. 10.
    Derjaguin, B.V., Abrikosova, I.I.: JETP 3, 819 (1957)Google Scholar
  11. 11.
    blocki, J., Swiatecki, W.J.: Ann. Phys. (N. Y.) 132, 53 (1981)ADSCrossRefGoogle Scholar
  12. 12.
    Schaden, M., Spruch, L.: Phys. Rev. A 58, 935 (1998)ADSCrossRefMATHGoogle Scholar
  13. 13.
    Schaden, M., Spruch, L.: Phys. Rev. Lett. 84, 459 (2000)ADSCrossRefGoogle Scholar
  14. 14.
    Jaffe, R.L., Scardicchio, A.: Phys. Rev. Lett. 92, 070402 (2004)ADSCrossRefGoogle Scholar
  15. 15.
    Scardicchio, A., Jaffe, R.L.: Nucl. Phys. B 704, 552 (2005)MathSciNetADSCrossRefMATHGoogle Scholar
  16. 16.
    Scardicchio, A., Jaffe, R.L.: Nucl. Phys. B 743, 249 (2006)MathSciNetADSCrossRefMATHGoogle Scholar
  17. 17.
    Gies, H., Langfeld, K., Moyaerts, L.: JHEP 0306, 018 (2003)MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    Gies, H., Klingmuller, K.: Phys. Rev. Lett. 96, 220401 (2006)ADSCrossRefGoogle Scholar
  19. 19.
    Gies, H., Klingmuller, K.: Phys. Rev. Lett. 97, 220405 (2006)ADSCrossRefGoogle Scholar
  20. 20.
    Gies, H., Klingmuller, K.: Phys. Rev. D 74, 045002 (2006)ADSCrossRefGoogle Scholar
  21. 21.
    Bordag, M.: Phys. Rev. D 73, 125018 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    Bulgac, A., Magierski, P., Wirzba, A.: Phys. Rev. D 73, 025007 (2006)ADSCrossRefGoogle Scholar
  23. 23.
    Emig, T., Jaffe, R.L., Kadar, M., Scardicchio, A.: Phys. Rev. Lett. 96, 080403 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    Emig, T., Graham, N., Jaffe, R.L., Kardar, M.: Phys. Rev. Lett. 99, 170403 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    Emig, T., Graham, N., Jaffe, R.L., Kardar, M.: Phys. Rev. D 77, 025005 (2008)ADSCrossRefGoogle Scholar
  26. 26.
    Emig, T., Jaffe, R.L.: J. Phys. A 41, 164001 (2008)MathSciNetADSCrossRefGoogle Scholar
  27. 27.
    Milton, K.A., Wagner, J.: J. Phys. A 41, 155402 (2008)MathSciNetADSCrossRefGoogle Scholar
  28. 28.
    Rahi, S.J., Emig, T., Graham, N., Jaffe, R.L., Kardar, M.: Phys. Rev. D 80, 085021 (2009)ADSCrossRefGoogle Scholar
  29. 29.
    Dalvit, D.A.R., Lombardo, F.C., Mazzitelli, F.D., Onofrio, R.: Phys. Rev. A 74, 020101(R) (2006)ADSCrossRefGoogle Scholar
  30. 30.
    Mazzitelli, F.D., Dalvit, D.A.R., Lombardo, F.C.: New J. Phys. 8, 240 (2006)ADSCrossRefGoogle Scholar
  31. 31.
    Kaluza, T.: Sitz. Preuss. Akad. Wiss. Phys. Math. K1, 966 (1921)Google Scholar
  32. 32.
    Klein, O.: Z. Phys. 37, 895 (1926)ADSCrossRefMATHGoogle Scholar
  33. 33.
    Randall, L., Sundrum, R.: Phys. Rev. Lett. 83, 3370 (1999)MathSciNetADSCrossRefMATHGoogle Scholar
  34. 34.
    Randall, L., Sundrum, R.: Phys. Rev. Lett. 83, 4690 (1999)MathSciNetADSCrossRefMATHGoogle Scholar
  35. 35.
    Poppenhaeger, K., Hossenfelder, S., Hofmann, S., Bleicher, M.: Phys. Lett. B 582, 1 (2004)ADSCrossRefGoogle Scholar
  36. 36.
    Cheng, H.: Chin. Phys. Lett. 22, 2190 (2005)ADSCrossRefGoogle Scholar
  37. 37.
    Cheng, H.: Mod. Phys. Lett. A21, 1957 (2006)ADSCrossRefGoogle Scholar
  38. 38.
    Cheng, H.: Phys. Lett. B 643, 311 (2006)ADSCrossRefGoogle Scholar
  39. 39.
    Cheng, H.: Phys. Lett. B 668, 72 (2008)ADSCrossRefGoogle Scholar
  40. 40.
    Edery, A., Marachevsky, V.: JHEP 0812, 035 (2012)ADSGoogle Scholar
  41. 41.
    Fulling, S.A., Kirsten, K.: Phys. lett. B 671, 179 (2009)ADSCrossRefGoogle Scholar
  42. 42.
    Kirsten, K., Fulling, S.A.: Phys. D 79, 065019 (2009)MathSciNetGoogle Scholar
  43. 43.
    Elizalde, E., Odintsov, S.D., Saharian, A.A.: Phys. Rev. D 79, 065023 (2009)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of PhysicsEast China University of Science and TechnologyShanghaiChina
  2. 2.The Shanghai Key Laboratory of AstrophysicsShanghaiChina

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