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On the dibaryon ansatz in nonlinear sigma models: Review, developments and problems

Abstract

I present a short review, focussing on five points of view, of the dibaryon ansatz, which plays an important role in the study of nonlinear sigma models, and propose new problems concerning this ansatz.

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References

  1. 1.

    Skyrme, T. H. R., A non-linear field theory. Proc. Roy. Soc. London A260, 127–138 (1961); Skyrme, T. H. R., A unified field theory of mesons and baryons, Nucl. Phys. 31, 556–569 (1962); Adkins, G., Nappi, C. R., and Witten, E., Static properties of nucleons in the Skyrme model, Nucl. Phys. B228, 552–564 (1984).

  2. 2.

    Chodos, A. et al., Solitons in Nuclear and Elementary Particle Physics, World Science, Singapore, 1984.

  3. 3.

    Balachandran, A. P., Barducci, A., Lizzi, F., Rodgers, V. G. J., and Stern, A., Doubly strange dibaryon in the chiral model, Phys. Rev. Lett. 52, 887–890 (1984); Balachandran, A. P., Lizzi, F., Rodgers, V. G. J., and Stern, A., Dibaryons as chiral solitons, Nucl. Phys. B256, 525–556 (1985).

  4. 4.

    Palais, R., The principle of symmetric criticality, Commun. Math. Phys. 69, 19–30 (1979).

  5. 5.

    Witten, E., Non-Abelian bosonization in two dimensions, Commun. Math. Phys. 92, 455–472 (1984); Witten, E., Global aspects of current algebra, Nucl. Phys. B223, 422–432 (1983); Witten, E., Current algebra, baryons, and quark confinement, Nucl. Phys. B223, 433–444 (1983).

  6. 6.

    Braaten, E., Curtright, T. L., and Zachos, C. K., Torsion and geometrostasis in nonlinear sigma models, Nucl. Phys. B260, 630–688 (1985).

  7. 7.

    Date, H., Fujii, K., and So, H., Extended Skyrme models in even dimensions and higher dimensional solitons, Lett. Math. Phys. 13, 195–200 (1987); Fujii, K., So, H., and Suwa, M., Extended Skyrme models in even dimensions and higher dimensional solitons II: Calculations of Wess-Zumino terms in two and higher dimensions, Lett. Math. Phys. 15, 151–158 (1988).

  8. 8.

    Witten, E., Some exact multipseudoparticle solutions of classical Yang-Mills Theory, Phys. Rev. Lett. 38, 121–124 (1977).

  9. 9.

    Actor, A., Classical solution of SU(2) Yang-Mills theories, Rev. Mod. Phys. 51, 461–525 (1979).

  10. 10.

    't Hooft, G., Magnetic monopoles in unified gauge theories, Nucl. Phys. B79, 276–284 (1974); Polyakov, A. M., JETP Lett. 20, 194–195 (1974).

  11. 11.

    The result of this section was obtained by suggestion of Profs H. Ôike and S. Watanabe at Yamagata University. I thank them sincerely.

  12. 12.

    Fujii, K., Otsuki, S., and Toyoda, F., A soliton solution with baryon number B=0 and skyrmion, Prog. Theor. Phys. 73, 524–527 (1985); Fujii, K., Otsuki, S., and Toyoda, F., Solitons with the Hopf index versus skyrmions in SU(2) nonlinear sigma model, Prog. Theor. Phys. 73, 1287–1290 (1985).

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Partially supported by the Grant-in-Aid for Scientific Research No. 61460005.

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Fujii, K. On the dibaryon ansatz in nonlinear sigma models: Review, developments and problems. Lett Math Phys 16, 365–375 (1988). https://doi.org/10.1007/BF00402045

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Keywords

  • Statistical Physic
  • Group Theory
  • Sigma Model
  • Short Review
  • Nonlinear Sigma Model