Skip to main content
SpringerLink
Log in

The spectrum-generating groups program and the string

  • Part V. Invited Papers Commemorating The Centenary Of The Birth Of Erwin Schrödinger
  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

Schrödinger's approach was analytical, but it is equivalent to an algebraic treatment. We review the evolution of group theory as a physical tool and its application to the Hilbert space of Schrödinger's eigenstates. Special emphasis is put on recent results relating to the relativistic quantized string.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. A. Kastrup, inSymmetries in Physics (1600–1980), M. Garcia Doncel, ed.,Proceedings, Conference at Sant Feliu de Guixols, 1983, in press.

  2. L. A. Radicati,ibid.

  3. Emmy Noether,Nachr. Konigl. Ges. Wiss. Gött., Mat.-Phys. Kl., 235–257 (1918).

  4. D. Horn,Ann. Phys. (N.Y.) 32, 444 (1965).

    Google Scholar 

  5. D. Schechtman, I. Bleeh, D. Gratias, and J. W. Cahn,Phys. Rev. Lett. 53, 1951 (1984).

    Google Scholar 

  6. I. Ozsvath and E. Schucking, inRecent Developments in General Relativity (Infeld Festschrift) (Pergamon, New York, Oxford, 1962), p. 339.

    Google Scholar 

  7. C. Becchi, A. Rouet, and R. Stora,Ann. Phys. (N.Y.) 98, 287 (1976); I. V. Tyupin, Lebedev Proceedings (unpublished), FIAN, Vol. 39.

    Google Scholar 

  8. J. Thierry-Mieg,J. Math. Phys. 21, 2834 (1980);Nuovo Cimento A 56, 396 (1980); Y. Ne'eman and J. Thierry-Mieg,Proc. Natl. Acad. Sci. USA77, 720 (1980).

    Google Scholar 

  9. H. Weyl,Z. Phys. 56, 330 (1929).

    Google Scholar 

  10. E. P. Wigner,Ann. Math. 40, 149 (1939).

    Google Scholar 

  11. A. Cant and Y. Ne'eman,J. Math. Phys. 26, 3180 (1985).

    Google Scholar 

  12. W. Pauli,Z. Phys. 36, 336 (1926).

    Google Scholar 

  13. E. Schrödinger,Ann. Phys. (Leipzig) (4)79, 489 (1926);79, 734 (1926).

    Google Scholar 

  14. M. Gell-Mann and Y. Ne'eman,The Eightfold Way (W. A. Benjamin, New York, 1964).

    Google Scholar 

  15. F. J. Dyson,Symmetry Groups in Nuclear and Particle Physics (Benjamin, New York, 1966).

    Google Scholar 

  16. Y. Dothan, M. Gell-Mann, and Y. Ne'eman,Phys. Lett. 17, 1107 (1965).

    Google Scholar 

  17. A. Bohm and A. O. Barut,Phys. Rev. B 139, 1107 (1965).

    Google Scholar 

  18. Y. Dothan and Y. Ne'eman, inResonant Particles, (Proceedings, Athens, Ohio Conference, 1965), B. A. Munir, ed., (University of Ohio, Athens and Fazl-i-umar Research Institute, Athens, Ohio (1965), p. 17); reprinted in Ref. 15, p. 279; Y. Ne'eman,Algebraic Theory of Particle Physics (Benjamin, New York, 1967), p. 287.

    Google Scholar 

  19. A. O. Barut,Phys. Rev. B 139, 1433 (1965).

    Google Scholar 

  20. J. P. Elliott,Proc. R. Soc. London A 245, 128, (1958).

    Google Scholar 

  21. S. Goshen and H. J. Lipkin,Ann. Phys. (N.Y.)6, 301 (1959).

    Google Scholar 

  22. A. O. Barut, inSymmetry Principles at High Energy (Proceedings, 1964 Coral Gables Conference), B. Kursunoglu and A. Perlmutter, eds. (Freeman, San Francisco, 1964), p. 81.

    Google Scholar 

  23. L. O'Raifeartaigh,Phys. Rev. Lett. 14, 332, 575 (1965).

    Google Scholar 

  24. Y. Dothan,Phys. Rev. D 2, 2944 (1970).

    Google Scholar 

  25. D. W. Joseph, “Representations of the Algebra of SL(3,R) with |ΔJ| = 2,” University of Nebraska preprint, 1969.

  26. L. C. Biedenharn, R. Y. Cusson, M. Y. Han, and O. L. Weaver,Phys. Lett. B 42, 257 (1972).

    Google Scholar 

  27. G. Rosensteel and D. J. Rowe,Ann. Phys. (N.Y.) 123, 36 (1979);126, 198, 343 (1980).

    Google Scholar 

  28. A. Arima and F. Iachello,Annu. Rev. Nucl. Part. Sci. 31, 75 (1981).

    Google Scholar 

  29. Y. Alhassid, F. Iachello, and J. Wu,Phys. Rev. Lett. 56, 271 (1986).

    Google Scholar 

  30. A. Bohm,Phys. Rev. 175, 1767 (1968);D 3, 377 (1971).

    Google Scholar 

  31. Y. Ne'eman,Ann. Inst. Henri Poincaré, Sec. A. 28, 369 (1978);Proc. Natl. Acad. Sci. U.S.A. 74, 4157 (1977).

    Google Scholar 

  32. Y. Ne'eman and Dj. Šijački,Int. J. Mod. Phys. A 2, 1655 (1987).

    Google Scholar 

  33. Y. Ne'eman and Dj. Šijački,J. Math. Phys. 26, 2457 (1985).

    Google Scholar 

  34. Y. Ne'eman and Dj. Šijački,Phys. Lett. B 157, 267 (1985).

    Google Scholar 

  35. Y. Ne'eman and Dj. Šijački,Phys. Lett. B 157, 275 (1985).

    Google Scholar 

  36. R. F. Dashen and M. Gell-Mann,Phys. Rev. Lett. 17, 340 (1966).

    Google Scholar 

  37. S. J. Chang, R. F. Dashen, and L. O'Raifeartaigh,Phys. Rev. 182, 1805 (1969).

    Google Scholar 

  38. S. L. Adler and R. F. Dashen,Current Algebra (Benjamin, New York, 1968).

    Google Scholar 

  39. J. Mehra and H. R. Rechenberg,The Historical Development of Quantum Theory, Vol. 2, (Springer, New York, 1986), p. 246.

    Google Scholar 

  40. V. de Alfaro, S. Fubini, G. Rossetti, and G. Furlan,Phys. Lett. 21, 576 (1966).

    Google Scholar 

  41. R. Dolen, D. Horn, and C. Schmid,Phys. Rev. Lett. 19, 402 (1967); A. A. Logunov, L. D. Soloviev, and A. Tavkhelidze,Phys. Lett. B 24, 181 (1967); K. Igi and S. Matsuda,Phys. Rev. Lett. 18, 625 (1967).

    Google Scholar 

  42. P. G. O. Freund,Phys. Rev. Lett. 20, 235 (1968); H. Harari,Phys. Rev. Lett. 20, 1395 (1968).

    Google Scholar 

  43. H. Harari,Phys. Rev. Lett. 22, 562 (1969); J. Rosner,Phys. Rev. Lett. 22, 689 (1969).

    Google Scholar 

  44. G. Veneziano,Nuovo Cimento A 57, 190 (1968).

    Google Scholar 

  45. Y. Nambu, inSymmetries and Quark Models, (Proceedings Wayne State 1969 Conference), R. Chand, ed., (Gordon & Breach, New York, 1970), p. 269; L. Susskind,Nuovo Cimento 69, 457 (1970); H. Nielsen, 15th Int. Conf. High Energy Physics (Kiev, 1970).

    Google Scholar 

  46. A. Neveu and J. H. Schwarz,Nucl. Phys. B 31, 86 (1971); P. Ramond,Phys. Rev. D 3, 2415 (1971).

    Google Scholar 

  47. M. B. Green and J. H. Schwarz,Nucl. Phys. B 181, 502 (1981);Phys. Lett. 109B, 444 (1982).

    Google Scholar 

  48. D. J. Gross, J. A. Harvey, E. Martinec and R. Rohm,Phys. Rev. Lett. 54, 502 (1985).

    Google Scholar 

  49. T. Piran and S. Weinberg, eds.,Physics in Higher Dimensions, (2nd Jerusalem Winter School, 1984/5), (World Scientific, Singapore, 1985).

    Google Scholar 

  50. I. B. Frenkel and V. G. Kac,Inventiones Math. 62, 23 (1980).

    Google Scholar 

  51. S. Coleman and J. Mandula,Phys. Rev. 159, 1251 (1967).

    Google Scholar 

  52. R. Haag, J. T. Lopuszanski and M. F. Sohnius,Nucl. Phys. B 88, 257 (1975).

    Google Scholar 

  53. D. Friedan, Z. Qiu and S. Shenker, inVertex Operators in Mathematics and Physics, J. Lepowsky, S. Mandelstam, and I. M. Singer, eds., (Springer-Verlag, New York, Berlin, Heidelberg, Tokyo 1985), p. 419.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Raymond and Beverley Sackler Faculty of Exact Sciences, Wolfson Chair Extraordinary in Theoretical physics, Tel Aviv University, Tel Aviv, Israel

    Yuval Ne'eman

Authors
  1. Yuval Ne'eman
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to the 100th anniversary of the birth of Erwin Schrödinger. Invited Lecture at the 1987 Washington APS Meeting, Symposium on Dynamical Symmetries.

Also on leave from the Center for Particle Theory, University of Texas, Austin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ne'eman, Y. The spectrum-generating groups program and the string. Found Phys 18, 245–275 (1988). https://doi.org/10.1007/BF01891492

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01891492

Keywords

Search

Navigation