Skip to main content

Part of the book series: Studies in the Natural Sciences ((SNS,volume 13))

  • 119 Accesses

Abstract

A review of some recent work on the collective coordinate approach to perturbation expansion about soliton solutions is presented. Consistent formulation of the method in framework of the Feynman path integral quantization procedure is described. As an illustrative application we discuss in detail a perturbation expansion for scattering of solitons.

Research sponsored by the Energy Research and Development Administration Grant No. E(11-1)-2220.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Dashen, B. Hasslacher and A. Neveu, Phys. Rev. D 10, 4114 (1974);

    Article  ADS  Google Scholar 

  2. R. Dashen, B. Hasslacher and A. Neveu, Phys. Rev. D 10, 4130 (1974).

    Article  ADS  Google Scholar 

  3. J. L. Gervais and B. Sakita, Phys. Rev. D 11, 2943 (1975)

    Article  ADS  Google Scholar 

  4. J. L. Gervais, A. Jevicki and B. Sakita, Phys. Rev. D. 12, 1038 (1975).

    Article  ADS  Google Scholar 

  5. For an entirely different approach see: J. Goldstone and R. Jackiw, Phys. Rev. D 11, 1486 (1975).

    Article  ADS  Google Scholar 

  6. C. Callan and D. Gross, Nucl. Phys. B 93, 29 (1975).

    Article  ADS  Google Scholar 

  7. L. D. Faddeev, V. E. Korepin and P. P. Kulish, JETP Lett. 21, 260 (1975).

    Google Scholar 

  8. J. L. Gervais, A. Jevicki and B. Sakita, Phys. Reports 23, 237 (1976);

    Article  ADS  Google Scholar 

  9. see also A. Hosoya and K. Kikkawa Nucl. Phys. B 101, 271 (1976).

    Article  ADS  Google Scholar 

  10. J. L. Gervais and A. Jevicki, Nucl. Phys. B 110, 93 (1976).

    Article  MathSciNet  ADS  Google Scholar 

  11. E. Tomboulis, Phys. Rev. D 12, 1678 (1975),

    Article  ADS  Google Scholar 

  12. N. Christ and T. D. Lee, Phys. Rev. D 12, 1606 (1975).

    Article  MathSciNet  ADS  Google Scholar 

  13. J. L. Gervais and A. Jevicki, Nucl. Phys. B 110, 113 (1976);

    Article  MathSciNet  ADS  Google Scholar 

  14. for the discussion of N-soliton scattering see A. Jaeckel, Ecole Normal preprint (1976).

    Google Scholar 

  15. R. Jackiw and G. Woo, Phys. Rev. D 12, 1643 (1975).

    Article  MathSciNet  ADS  Google Scholar 

  16. R. Dashen, B. Hasslacher and A. Neveu, Phys. Rev. D 11, 3424 (1975).

    Article  MathSciNet  ADS  Google Scholar 

  17. V. C. Korepin, JETP Lett. 23, 224 (1976);

    Google Scholar 

  18. for the “complex time” method see D. McLaughlin, J. Math. Phys. 13, 1099 (1972).

    Article  MathSciNet  ADS  Google Scholar 

  19. A. Jevicki, Nucl. Phys. B 117, 365 (1976).

    Article  ADS  Google Scholar 

  20. L. D. Faddeev and V. E. Korepin, Phys. Lett. 63B, 435 (1976); similar propagators appear also in the classical perturbation expansion for solitons developed by J. Keener and D. McLaughlin (preprint 1976).

    ADS  Google Scholar 

  21. The only higher loop calculation performed so far is the two-loop correction to soliton mass in the Sine-Gordon theory; H. deVega, Nucl. Phys. B 115, 411 (1975).

    Article  ADS  Google Scholar 

  22. G. ’t Hooft, Phys. Rev. D 14, 3432 (1976); A. Polyakov Nordita preprint (1976);

    Article  ADS  Google Scholar 

  23. E. Brezin, J. C. Le Guillou and J. Zinn-Justin, Saclay preprint (1976).

    Google Scholar 

  24. A. A. Belavin, A. M. Polyakov, A. S. Schwartz and Yu. S. Tyupkin, Phys. Lett. 59B, 85 (1975).

    MathSciNet  ADS  Google Scholar 

  25. J. L. Gervais and B. Sakita, CCNY preprint (1976).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Plenum Press, New York

About this chapter

Cite this chapter

Jevicki, A. (1977). Path Integral Quantization of Solitons. In: Perlmutter, A., Scott, L.F. (eds) The Significance of Nonlinearity in the Natural Sciences. Studies in the Natural Sciences, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-7224-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-7224-0_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-7226-4

  • Online ISBN: 978-1-4684-7224-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics