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Self-Dual Chern—Simons Solitons

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Mathematical Physics X

Abstract

These lectures are devoted to the two-year old topic of Chern-Simons solitons. Solitons have interested particle theorists since the mid-1970’s[1]; Chern-Simons dynamics, since the early 1980’s [2]. Now in the decade of the 1990’s, we are combining the two subjects.

This work is supported in part by funds provided by the U. S. Department of Energy (D.O.E.) under contract #DE-AC02–76ER03069.

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References

  1. For reviews see Jackiw, R.: Rev.Modern Phys. 49, 681 (1977);

    Article  MathSciNet  ADS  Google Scholar 

  2. Rajaraman, R.: Solitons and Instantons. North Holland, Amsterdam, 1982

    MATH  Google Scholar 

  3. Jackiw, R., Templeton, S.: Phys.Rev. D 23, 2291 (1981);

    Article  ADS  Google Scholar 

  4. Schonfeld, J.: Nuclear Phys. B 185, 157 (1981);

    Article  ADS  Google Scholar 

  5. Deser, S., Jackiw, R., Templeton, S.: Phys.Rev.Lett. 48, 975 (1982);

    Article  ADS  Google Scholar 

  6. Deser, S., Jackiw, R., Templeton, S.: Ann. Physics (NY) 140, 372 (1982);

    Article  MathSciNet  ADS  Google Scholar 

  7. Deser, S., Jackiw, R., Templeton, S.: Ann. Physics (E) 185, 406 (1988)

    Article  MathSciNet  Google Scholar 

  8. Jackiw, R., Pi, S.-Y.: Phys.Rev.Lett. 64, 2969 (1990);

    Article  MathSciNet  MATH  ADS  Google Scholar 

  9. Jackiw, R., Pi, S.-Y.: Phys.Rev.Lett. (C) 66, 2682 (1991);

    Article  MathSciNet  ADS  Google Scholar 

  10. Jackiw, R., Pi, S.-Y.: Phys.Rev. D 42, 3500 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  11. Hagen, C.: Ann.Physics (NY) 157, 342 (1984);

    Article  MathSciNet  ADS  Google Scholar 

  12. Hagen, C.: Phys.Rev. D 31, 848, 2135 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  13. Takagi, S.: Progr.Theoret.Phys. 84, 1019 (1990);

    Article  ADS  Google Scholar 

  14. Takagi, S.: Progr.Theoret.Phys. 85, 463, 723 (1991);

    Article  MathSciNet  ADS  Google Scholar 

  15. Takagi, S.: Tohoku University preprint (June 1991)

    Google Scholar 

  16. This conformai symmetry of non-relativistic dynamics was discussed in the early seventies, when conformai symmetry of relativistic theories was explored in connection with deep inelastic scattering. Jackiw, R.: Physics Today 25, Nov. 1, 23 (1972);

    Article  ADS  Google Scholar 

  17. Hagen, C.: Phys.Rev. D 5, 377 (1972);

    Article  ADS  Google Scholar 

  18. Niederer, U.: Helv.Phys.Acta 45, 802 (1972);

    MathSciNet  Google Scholar 

  19. Niederer, U.: Helv.Phys.Acta 46, 191 (1073);

    Google Scholar 

  20. Niederer, U.: Helv.Phys.Acta 47, 119, 167 (1974);

    MathSciNet  Google Scholar 

  21. Niederer, U.: Helv.Phys.Acta 51, 220 (1978).

    MathSciNet  Google Scholar 

  22. In the context of Chern-Simopns dynamics, the symmetry was identified in Jackiw, R.: Ann.Physics (NY) 201, 83 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  23. Jackiw, R.: Bég Memorial Volume (World Scientific, Singapore). In press, MIT preprint CTP#1937 (January, 1991)

    Google Scholar 

  24. These issues are under further investigation by O. Bergman (in preparation)

    Google Scholar 

  25. de Alfaro, V., Fubini, S., Furlan, G.: Nuovo Cimento A A34, 569 (1976);

    Article  ADS  Google Scholar 

  26. Jackiw, R.: Ann.Physics (NY) 129, 183 (1980) and last entry Ref. [6]; Takagi, Ref. [5]

    Article  MathSciNet  ADS  Google Scholar 

  27. The idea of generating time-dependent solitons from static solitons by these transformations is due to Ezawa, Z., Hotta, M., Iwazaki, A.: Phys.Rev.D 44, 452 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  28. Hotta, M.: Tohoku University preprint, TU-372 (July 1991)

    Google Scholar 

  29. Freedman, D., Newell, A.: (unpublished)

    Google Scholar 

  30. Kim, S., Soh, K., Yee, J.: Phys.Rev. D 42, 4139 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  31. Olesen, P.: Phys.Lett. B 265, 361 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  32. Davey, A., Stewartson, K.: Proc.Roy.Soc. London Ser.A 338, 101 (1974);

    Article  MathSciNet  MATH  ADS  Google Scholar 

  33. Anker, D., Freeman, N.: Proc.Roy.Soc. London Ser.A 360, 529 (1978)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  34. Jackiw, R., Pi, S.-Y.: Phys.Rev.D 44, xxx (1991) and Ref. [3]

    Article  MathSciNet  Google Scholar 

  35. Jackiw, R., Pi, S.-Y.: Phys.Rev.D 44, xxx (1991)

    Article  MathSciNet  Google Scholar 

  36. Jackiw, R., Pi, S.-Y.: Phys. Rev. Lett. 67, 415 (1991) and Ref. [16]

    Article  MathSciNet  MATH  ADS  Google Scholar 

  37. Ezawa, Z., Hotta, M., Iwazaki, A.: Phys.Rev.Lett. 67, 411 (1991) and Ref. [10]

    Article  MathSciNet  MATH  ADS  Google Scholar 

  38. Grossman, B.: Phys.Rev.Lett. 65, 3230 (1990)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  39. Dunne, G., Jackiw, R., Pi, S.-Y., Trugenberger, C.: Phys.Rev.D 43, 1332 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  40. Ward, R.: Philos.Trans.Roy.Soc. London Ser.A A315, 451 (1985);

    Article  ADS  Google Scholar 

  41. Hitchin, N.: Proc.Math.Soc. London 55, 59 (1987);

    Article  MathSciNet  MATH  Google Scholar 

  42. Donaldson, S.: Proc.Math.Soc. London 55, 127 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  43. Yoon, Y.: Ann.Physics (NY) 211, 316 (1991)

    Article  MATH  ADS  Google Scholar 

  44. Hong, J., Kim, Y., Pac, P.Y.: Phys.Rev.Lett. 64, 2230 (1990)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  45. Jackiw, R., Weinberg, E.: Phys.Rev.Lett. 64, 2234 (1990);

    Article  MathSciNet  MATH  ADS  Google Scholar 

  46. Jackiw, R., Lee, K., Weinberg, E.: Phys.Rev. D 42, 3488 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  47. Lee, C., Lee, K., Weinberg, E.: Phys.Lett. B 243, 105 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  48. Khare, A.: Phys.Lett. B 225, 393 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  49. Spruck, J., Yang, Y.: (preprint 1991); Ren, H., Weinberg, E.: (in preparation)

    Google Scholar 

  50. Wang, R.: Comm.Math.Phys. 137, 587 (1991)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  51. Integrability of this equation and its generalizations when the spatial geometry is not flat have been examined by Schiff, J.: J.Math.Phys. 32, 753 (1991)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  52. Kim, S., Min, H.: Seoul National University preprint SNU TP 91–41 (1991)

    Google Scholar 

  53. Kabat, D.: MIT preprint CTP#2016 (September 1991)

    Google Scholar 

  54. Ïpekoğlu, Y., Leblanc, M., Thomaz, M.T.: Ann.Physics (NY) (in press)

    Google Scholar 

  55. Non-relativistic matter dynamics: Dunne, G., Trugenberger, C.: Phys. Rev. D 43, 1323 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  56. Relativistic matter dynamics: Lee, C., Lee, K., Min, H.: Phys.Lett. B 252, 79 (1990);

    Article  MathSciNet  ADS  Google Scholar 

  57. Lee, C., Min, H., Rim, C.: Seoul National University preprint SNU TP 90–39 (1990);

    Google Scholar 

  58. Lee, J., Nam, S.: Phys.Lett. B 261, 437 (1991)

    Article  ADS  Google Scholar 

  59. Lee, K.: Phys.Lett. B 255, 381 (1991);

    Article  MathSciNet  ADS  Google Scholar 

  60. Lee, K.: Phys.Rev.Lett. 66, 553 (1991)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  61. Lee,J., Nam, S.: Ref. [33]; Yang, Y.: Lett.Math.Phys. (in press)

    Google Scholar 

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© 1992 Springer-Verlag Berlin Heidelberg

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Jackiw, R. (1992). Self-Dual Chern—Simons Solitons. In: Schmüdgen, K. (eds) Mathematical Physics X. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77303-7_15

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  • DOI: https://doi.org/10.1007/978-3-642-77303-7_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-77305-1

  • Online ISBN: 978-3-642-77303-7

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