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Hybridizing the skyrmion with an anti-de-sitter bag

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Il Nuovo Cimento B (1971-1996)

Summary

We discuss a phenomenological model of the nucleon in which a small anti-de-Sitter bag is placed into the skyrmion configuration. Such a bag has a timelike boundary and allows naturally the Cheshire Gat Principle. Very important in this model is the membrane of the bag, the 3-dimensional manifoldS 1 }xS 2, in which topological techniques will come into play.

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References

  1. A. W. Thomas:Prog. Theor. Phys. Suppl.,91, 204 (1987).

    Article  ADS  Google Scholar 

  2. V. I. Sanyuk:Genesis and Evolution of the Skyrme Model from 1954 to the Present, preprint SU-4228-465 (1990); E. H. Lieb:Remarks on the Skyrme model, Lecture given at the 1990 Summer Institute on Differential Geometry (1990); C. L. Terng:Ann. Math.,111, 491 (1980); N. Joshi:Lett. Math. Phys.,20, 261 (1990); L. D. Fadeev:Lett. Math. Phys.,1, 289 (1976); Y. Yang:J. Math. Phys.,30, 824 (1989); I. Zahed and G. E. Brown:Phys. -Rep.,142, 1 (1986); P. J. Mulders:Phys. Rev.,30, 1073 (1984).

  3. E. Witten:Nucl. Phys. B,160, 57 (1979); L.-H. Chan:Phys. Rev. Lett,55, 21 (1985);57, 1199 (1986).

    Article  ADS  Google Scholar 

  4. T. H. R. Skyrme:Proc. R. Soc. London, Ser. A,260, 127 (1961); H. Date, K. Fujii and H. So:Lett. Math. Phys.,13, 195 (1987).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. E. Witten:Nucl. Phys. B,223, 422 (1983); S. Vadia: inLect. Notes Phys.,208 (Springer, 1984).

    Article  ADS  MATH  Google Scholar 

  6. G. E. Brown: inProceedings of the International Conference on Nuclear Physics, Florence, Italy (Pergamon, New York, N.Y., 1983).

    Google Scholar 

  7. S. Nadkarni, H. B. Nielsen andI. Zahed:Nucl. Phys. B,253, 308 (1985).

    Article  ADS  Google Scholar 

  8. H. Rosu: preprint FT-337 (1988);Rev. Roum. Phys.,34, 1239 (1988).

  9. A. S. Eddington:The Mathematical Theory of Relativity (Cambridge University Press, Cambridge, 1930); R. C. Tolman:Relativity, Thermodynamics and Cosmology (Oxford University Press, Oxford, 1934); L. Godeaux:Les geometries Cayleyennes et les universes d’Einstein et de de Sitter (Sciences et Lettres, Bruxelles, 1947); E. Schrödinger:Expanding Universes (Cambridge University Press, Cambridge, 1956), Schrödinger discusses in his book the elliptic interpretation obtained by identifing the antipodal points. In group theory terms, one would say the the AdS rotations have imprimitivity classes containing pairs of antipodal points; V. A. Fock:The Theory of Space, Time and Gravitation (Pergamon Press, New York, N.Y., 1959); H. P. Robertson and T. W. Noonan:Relativity and Cosmology (Saunders, Philadelphia, Penn., 1968); W. Rindler:Essential Relativity (Van Nostrand, Princeton, N.J., 1969); S. Weinberg:Gravitation and Cosmology (Wiley, New York, N.Y., 1972); S. W. Hawking and G. F. R. Ellis:The Large Scale Structure of Space and Time (Cambridge University Press, Cambridge, 1973); N. D. Birell and P. C. W. Davies:Quantum Fields in Curved Space (Cambridge University Press, Cambridge, 1982); N. A. Gromov:Contractions and Analytic Continuations of Classical Groups: A Unifying Treatment (in Russian, Syktyvkar, Novosibirsk, 1990); F. Gürsey: inGroup Theory Concepts and Methods in Elementary Particle Physics (Gordon and Breach, New York, N.Y., 1964); I. M. Yaglom et al.:Usp. Mat. Nauk,19, 51 (1964); R. I. Pimenov:Lith. Mat. Sb.,5, 457 (1965); W. Thirring:Acta Phys. Austriaca, Suppl. IV, 269 (1967); M. Gutzwiller:Helv. Phys. Acta,29, 313 (1956); N. A. Chernikov and E. A. Tagirov:Ann. Inst. H. Poincaré,9, 109 (1986); O. Nachtmann:Commun. Math. Phys.,6, 1 (1967); G. Börner and H. P. Dürr:Nuovo Cimento A,64, 669 (1967); O. Phillips and E. P. Wigner: inGroup Theory and its Applications, edited by E. M. Loebl (Academic Press, New York, N.Y., 1968); B. S. De Witt:Phys. Rep. C,19, 295 (1975); E. W. Mielke:Fortschr. Phys.,25, 401 (1977); G. Grensing:J. Phys. A,10, 1687 (1977); M. S. Drew:Ann. Phys.,103, 469 (1977); R. Drechsler and R. Sasaki:Nuovo Cimento A,46, 527 (1978); M. Henneaux and C. Teitelboim:Commun. Math. Phys.,98, 391 (1985); F. J. Herranz, M. A. del Olmo and M. Santander:Cayley-Klein geometries revisited, presented at theII International Wigner Symposium, Goslar, Germany, 1991.

    Google Scholar 

  10. P. Kerszberg:The Einstein-de Sitter controversy of 1916–1917 and the rise of relativistic cosmology, inEinstein Studies, Vol.1, edited by D. Howard and J. Stachel (Birkhauser, Berlin, 1989), p. 325.

    Google Scholar 

  11. J. Milnor:Bull. Am. Math. Soc.,6, 9 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Eiesland:Trans. Am. Math. Soc.,213, 213 (1925); S. Ianus:Stud. Cercet. Mat.,17, 1161 (1965).

    Article  MathSciNet  Google Scholar 

  13. B. Binegar, C. Fronsdal andW. Heidenreich:Ann. Phys.,149, 254 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  14. G. W. Gibbons:Aspects of Supergravity TheoriesThree Lectures in Spain, Barcelona, Spain, 1984.

  15. W. Heidenreich:Phys. Lett. B,110, 461 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  16. M. J. Duff, B. E. N. Nilsson andC. N. Pope:Phys. Rep.,130, 1 (1986).

    Article  MathSciNet  ADS  Google Scholar 

  17. E. Angelopoulos: inQuantum Theory, Groups, Fields and Particles, edited by A. O. Barut (Reidel, New York, N.Y., 1983), p. 101.

    Chapter  Google Scholar 

  18. H. Nicolai: preprint CERN TH-3882 (1984).

  19. P. A. M. Dirac:J. Math. Phys.,4, 901 (1963).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. C. Fronsdal:Phys. Rev. D,26, 1988 (1982);35, 1262 (1987); M. Flato and C. Fronsdal:J. Math. Phys.,22, 1100 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  21. M. J. Duff:Supermembranes: the first 15 weeks, CERN-TH-4797 (1987).

  22. E. Bergshoeff et. ai:Phys. Lett. B,199, 69 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  23. M. Flato andC. Fronsdal:Phys. Lett. B,172, 412 (1986);Lett. Math. Phys.,20, 65 (1990);J. Math. Phys.,32, 524 (1991); M. Nakashima:Lett. Math. Phys.,18, 237 (1988).

    Article  ADS  Google Scholar 

  24. L. Castell andW. Heidenreich:Phys. Rev. D,24, 371 (1981);Acta Phys. Austriaca, Suppl. XXXIII, 605 (1981); H. Rumpf:Phys. Rev. D,24, 275 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  25. S. J. Avis, C. J. Isham andD. Storey:Phys. Rev. D,18, 3565 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  26. A short list of papers is the following:C. J. C. Burges et. al:Ann. Phys. (N.Y.),167, 285 (1986); B. Allenet al.:Phys. Lett. B,189, 304 (1987); D. Bernard and A. Folacci:Phys. Rev. D,34, 2286 (1986); R. Floreanini, C. T. Hill and R. Jackiw:Ann. Phys. (N.Y.),175, 354 (1987); P. Breitenlohner and D. Z. Freedman:Ann. Phys. (N.Y.),144, 249 (1982); S. Deser and R. Nepomechie:Ann. Phys. (N.Y.),154, 396 (1984); T. Inami and H. Ooguri:Progr. Theor. Phys.,73, 1051 (1985); E. S. Fradkin and M. A. Vasiliev:Ann. Phys. (N.Y.),177, 63 (1987).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. A. Bohm:Phys. Rev. D,33, 3358 (1986).

    Article  ADS  Google Scholar 

  28. K. S. Stelle andP. C. West:Phys. Rev. D,21, 1466 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  29. W. Miller jr.:Symmetry and separation of variables, inEnciclopedy of Mathematic and its Applications, edited by G.-C. Rota (Addison-Wesley, New York, N.Y., 1977).

    Google Scholar 

  30. B. Allen andM. Turyn:Nucl. Phys. B,292, 813 (1987).

    Article  ADS  Google Scholar 

  31. C. Sivaram andK. P. Sinha:Phys. Rep.,51, 111 (1979); S. I. Fisenkoet al:Phys. Lett. A,148, 405 (1990); E. Recami and V. Tonin-Zanchin: preprint INFN/AE-91/103 (1991); M. Kovalyov:Hadronic J.,12, 51 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  32. A. Salam andJ. Strathdee:Phys. Rev. D,18, 4596 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  33. R. Prasad:Nuovo Cimento A,44, 4327 (1966).

    Article  Google Scholar 

  34. Z. Haba:Phys. Lett. B,78, 421 (1978); C. C. Bernido: preprint IC/85/75 (1985).

    Article  ADS  Google Scholar 

  35. M. Romaniuk: inProceedings of the VIII Warsaw Symposium on Elementary Particle Physics (Kazimierz, Poland, 1985), p. 263.

    Google Scholar 

  36. E. Van Beveren, C. Dullemond andT. A. Rijken:Phys. Rev. D,30, 1103 (1984).

    Article  ADS  Google Scholar 

  37. N. Rosen:Gen. Rel. Grav.,12, 493 (1980); C. Dullemond:Gen. Rel. Grav.,20, 139 (1988).

    Article  ADS  MATH  Google Scholar 

  38. H. J. Bhabha:Nature (Suppl.) (18 Febr. 1939), p. 276.

  39. S. Fubini:Nuovo Cimento A,34, 521 (1976).

    Article  ADS  Google Scholar 

  40. P. Roman andJ. Haavisto:Int. J. Theor. Phys.,16, 915 (1977).

    Article  MathSciNet  Google Scholar 

  41. S. Coleman:Phys. Rev. D,11, 2088 (1975).

    Article  ADS  Google Scholar 

  42. M. Rho: Preprints SPhT/86–159 (1986), SPhT/84–123 (1984); R. J. Perry and M. Rho:Phys. Rev. D,34, 1169 (1986).

  43. S. Nadkarni andH. B. Nielsen:Nucl. Phys. B,263, 1 (1986). See also the following references: B.-Y. Park and V. Vento:Proton spin and the CCP, FTUV/90-50 (1990); H. B. Nielsenet al: Color anomaly in a hybrid bag model, Nordita-91/4 NP (1991);Workshop on skyrmions and Anomalies, Krakow (World Scientific, Singapore, 1987).

    Article  ADS  Google Scholar 

  44. H. B. Nielsen andA. Wirzba: preprint NBI-HE-87-32 (1987).

  45. J. Z. Imbrie et al:Comm. Math. Phys.,135, 421 (1991).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  46. W. Heidenreich:Phys. Rev. D,36, 1685 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  47. W. Weise:Nucl. Phys. A,434, 685c (1985): A. W. Thomas:Nucl. Phys. A,518, 186 (1990).

    Article  ADS  Google Scholar 

  48. L. Castell:Nuovo Cimento A,61, 585 (1968). See also: G. Börner:Progr. Theor. Phys.,43, 244 (1970).

    Article  MathSciNet  ADS  Google Scholar 

  49. C. J. Isham, A. Salam andJ. Strathdee:Phys. Rev. D,2, 685 (1970).

    Article  ADS  MATH  Google Scholar 

  50. Y. Shamir andS. H. Park:Phys. Lett. B,258, 179 (1991).

    Article  ADS  Google Scholar 

  51. T. Inami andH. Ooguri: preprint RIFP-612 (1985).

  52. Y. Verbin:Nucl. Phys. B,272, 739 (1986);Phys. Lett. B,197, 55 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  53. I. Klebanov:Nucl Phys. B,262, 133 (1985).

    Article  ADS  Google Scholar 

  54. J. David Brown andC. Teitelboim:Nucl. Phys. B,297, 787 (1988); Yu. E. Pokrovskii:Yad. Fiz.,50, 907 (1989); A. T. Barnaveli and O. V. Kancheli:Sov. J. Nucl. Phys.,52, 437 (1991); H. Sato:Prog. Theor. Phys.,76, 1250 (1986); J. Ipser and P. Sikivie:Phys. Rev. D,30, 712 (1984);42, 494 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  55. O. Heckman andE. Schücking:Handbuch der Physik,53 (Springer, Berlin, 1959), p. 515. See also the following list of mathematical papers: H. V. Fagundes:Closed spaces in cosmology, preprint IFT-P.013/91 (1991);Lett. Math. Phys.,6, 417 (1982); G. F. R. Ellis:Gen. Rel. Grav.,2, 7 (1971); L. A. Best:Can. J. Math.,23(3), 451 (1971); E. M. Andreev:Mat. Sb.,81, 445 (1970); E. B. Vinberg:Usp. Mat. Nauk,40, 29 (1985); I. S. Gutsul: TV.Mat. Inst. V. A. Steklov,152, 89 (1980); A. Yu. Vesnin:Sib. Mat. J.,28, 50 (1987); T. Jorgensen:Ann. Math.,106, 61 (1977); C. Weber and H. Seifert:Math. Z.,37, 237 (1933); P. Scott:Bull. London Math. Soc.,15, 401 (1983); C. Series:Interdiscip. Sci. Ren,15, 224 (1990); V. P. Frolov:Phys. Rev. D,43, 3878 (1991). In this paper the membraneS1 × S2 is treated as a compactified 3d space with one wormhole, being an example of a time machine. G. D. Mostow:Bull. Am. Math. Soc.,16, 225 (1987); J. P. Gaspard, R. Mosseri and J. F. Sadoc:Philos. Mag. B,45, 467 (1982); R. Mosseri and J. F. Sadoc:Philos. Mag. B,50, 557 (1984); A. N. Cyuvyrovet al: JETF,89, 2052 (1985); I. A. Ovidko:Ukr. Fiz. J.,34, 1343 (1989); A. M. Srivastava:Phys. Rev. D,43, 1047 (1991).

    Google Scholar 

  56. K. Yano andS. Böchner:Curvature and Betti Numbers (Purdue University Press, Lafayette, Ind., 1953).

    MATH  Google Scholar 

  57. R. T. Hammond andW. A. McKinley:Phys. Rev. D,20, 3047 (1979).

    Article  ADS  Google Scholar 

  58. V. G. Kadyshevsky andD. V. Fursaev:Teor. Mat. Fiz.,83, 197 (1990); G. A. Gal’perin:Dokl. Acad., Nauk.,302, 728 (1988) (Sov. Math. Dokl.,38, 367 (1989)); Yu. A. Golfand:JETF,43, 256 (1962).

    Google Scholar 

  59. B. Durand andI. Sarcevic:Phys. Rev. D,36, 2693 (1987).

    Article  ADS  Google Scholar 

  60. B. Allen andT. Jacobson:Comm. Math. Phys.,103, 669 (1986).

    Article  MathSciNet  ADS  Google Scholar 

  61. E. Calzetta, I. Jack andL. Parker:Phys. Rev. Lett,55, 1241 (1985).

    Article  MathSciNet  ADS  Google Scholar 

  62. P. Minkowski:Phys. Lett. B,173, 247 (1986).

    Article  MathSciNet  ADS  Google Scholar 

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On leave from Institute of Atomic Physics, P.O. Box MG-6, R-76900, Bucharest, Romania.

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Rosu, H. Hybridizing the skyrmion with an anti-de-sitter bag. Nuov Cim B 108, 313–329 (1993). https://doi.org/10.1007/BF02887491

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