Skip to main content

Part of the book series: NATO ASI Series ((NSSB,volume 349))

  • 280 Accesses

Abstract

These lectures review the important role of the Riemannian geometry of the moduli space (parameter space) of multi-defect field configurations in defect scattering. Also reviewed is one example of the statistical mechanics of a gas of defects, where the equation of state can be calculated using geometrical methods. The lectures conclude with some preliminary observations on the relevance of geometry in the dissipative dynamics of defects.

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. D’Eath, P., 1975 Phys. Rev. D12, 2183.

    ADS  Google Scholar 

  2. Manton, N.S., 1977 Nucl. Phys. B126, 525.

    Article  MathSciNet  ADS  Google Scholar 

  3. Bettencourt L.M.A. and Rivers, R.J., Imperial College preprint, 1994.

    Google Scholar 

  4. Skyrme, T.H.R., 1962 Nucl. Phys. 31, 556.

    Article  MathSciNet  Google Scholar 

  5. Jackson, A., Jackson, A.D. and Pasquier, V., 1985 Nucl. Phys. A432, 567; Manton, N.S., DAMTP preprint 94–84 (to appear in Acta Physica Polonica).

    Google Scholar 

  6. Schroers, B.J., 1994 Z. Phys. C61, 479.

    ADS  Google Scholar 

  7. Manton, N.S., 1985 Phys. Lett. 154B 397.

    MathSciNet  ADS  Google Scholar 

  8. Manton, N.S., 1982 Phys. Lett. 110B 54.

    MathSciNet  ADS  Google Scholar 

  9. Arnold, V.I., 1978 Mathematical Methods of Classical Mechanics, Springer-Verlag, New York.

    MATH  Google Scholar 

  10. Grabiak, M., Müller, B. and Greiner, W., 1986 Ann. Phys. 172, 213, and refs. therein.

    Google Scholar 

  11. Kim, Y. and Lee, K., 1994 Phys. Rev. D49, 2041.

    ADS  Google Scholar 

  12. Gibbons, G.W. and Manton, N.S., 1986 Nucl. Phys. B274, 183.

    Article  MathSciNet  ADS  Google Scholar 

  13. Bogomolny, E.B., 1976 Soy. J. Nucl. Phys. 24 449.

    Google Scholar 

  14. ’t Hooft, G., 1974 Nucl. Phys. B79 276; Polyakov, A.M., 1974 JETP Lett. 20 194; Prasad, M.K. and Sommerfield, C.M., 1975 Phys. Rev. Lett. 35 760.

    Google Scholar 

  15. Weinberg, E., 1979 Phys. Rev. D20 936.

    ADS  Google Scholar 

  16. Manton, N.S., 1988 Phys. Rev. Lett. 60 1916.

    Article  ADS  Google Scholar 

  17. Atiyah, M.F. and Manton, N.S. 1989 Phys. Lett. 222B 438; 1993 Commun. Math. Phys. 152, 391.

    Google Scholar 

  18. Stuart, D., 1994 Commum. Math. Phys. 159 51.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Stuart, D., U.C. Davis preprint, 1994.

    Google Scholar 

  20. Bates, L. and Montgomery, R., 1988 Commun. Math. Phys. 118, 635.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Manton, N.S. and Samols, T.M., 1988 Phys. Lett. 215B 559.

    MathSciNet  ADS  Google Scholar 

  22. Shellard, E.P.S. and Ruback, P.J.,1988 Phys. Lett. 209B 262; Moriarty, K.J.M., Myers, E. and Rebbi, C., 1988 Phys. Lett. 207B 411.

    Google Scholar 

  23. Samols, T.M., 1992 Commun. Math. Phys. 145, 149.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. Atiyah, M.F. and Hitchin, N.J., 1988 The geometry and dynamics of magnetic monopoles, Princeton U.P.

    Google Scholar 

  25. Wojtkowski, M.P., 1988 Bull. A.M.S. 18, 179; Temple-Raston, M. and Alexander, D., 1993 Nucl. Phys. B397 195.

    Google Scholar 

  26. Ward, R., 1985 Phys. Lett. 158B 424; Leese, R., 1990 Nucl. Phys. B344 33.

    Google Scholar 

  27. Ferrell, R.C. and Eardley, D.M., 1987 Phys. Rev. Lett. 59 1617; Gibbons, G.W. and Ruback, P.J., 1986 Phys. Rev. Lett. 57, 1492.

    Google Scholar 

  28. Shiraishi, K., 1993 Nucl. Phys. B402 399.

    Article  MathSciNet  ADS  Google Scholar 

  29. Strachan, I.A.B., 1992 J. Math. Phys. 33 102.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Shah, P.A., 1994 Nucl. Phys. B429 259.

    Article  ADS  Google Scholar 

  31. Leese, R., Manton, N.S. and Schroers, B.J., in preparation.

    Google Scholar 

  32. Manton, N.S., 1993 Nucl. Phys. B400[FS] 624.

    Google Scholar 

  33. Nielsen, H.B. and Olesen, P., 1973 Nucl. Phys. B61 45.

    Article  ADS  Google Scholar 

  34. Taubes, C., 1980 Commun. Math. Phys. 72, 277.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. Lamb, H. 1975 Hydrodynamics (6th ed. p.223), Cambridge U.P.

    Google Scholar 

  36. van Heijst, G.J.F. and Flór, J.B., 1989 Nature 340 212.

    Article  ADS  Google Scholar 

  37. Manton, N.S. and Shah, P.A., 1994 J. Math. Phys. 35 1171.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. Bradlow, S.B., 1990 Commun. Math. Phys. 135 1.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. Shah, P.A., DAMTP preprint 94–86.

    Google Scholar 

  40. Manton, N.S., unpublished.

    Google Scholar 

  41. Bray, A.J., Theory of phase ordering kinetics (to appear in Advances in Physics); Mazenko, G., these Proceedings

    Google Scholar 

  42. Goldenfeld, N., these Proceedings.

    Google Scholar 

  43. Chuang, I., Yurke, B., Pargellis, A. and Turok, N., 1993 Phys. Rev. E47, 3343.

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media New York

About this chapter

Cite this chapter

Manton, N. (1995). Geometry of Defect Scattering. In: Davis, AC., Brandenberger, R. (eds) Formation and Interactions of Topological Defects. NATO ASI Series, vol 349. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1883-9_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-1883-9_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5767-4

  • Online ISBN: 978-1-4615-1883-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics