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Prog. Theor. Phys. Vol. 24 No. 4 (1960) pp. 761-782

[ Full Text PDF : FREE ACCESS (1301K) ]

Internal Quantum States of Hyperspherical (Nakano) Relativistic Rotators

D. Bohm, P. Hillion* and J. P. Vigier*

Bristol University, England
*Institute Henri Poincaré, Paris, France

(Received February 29, 1960)

Abstract:

If one quantizes with conventional methods the classical internal motion of the hyperspherical (Nakano) relativistic rotator, the relativistic Hamiltonian splits into the sum of two complex conjugate spherical complex three-dimensional rotators. The corresponding excited “levels” also split into fine structure states, each "level" being naturally associated to a vector space irreducible under complex transformations isomorphic to the full Lorentz group. It finally turns out that every state is characterized by a set of quantum numbers with which we can classify typical families of rotator levels.


URL : http://ptp.ipap.jp/link?PTP/24/761/
DOI : 10.1143/PTP.24.761

[ Full Text PDF : FREE ACCESS (1301K) ] Citation:

References:

  1. D. Bohm, P. Hillion, T. Takabayasi and J. P. Vigier, Prog. Theor. Phys. 23 (1960), 496[PTP].
  2. D. Bohm and J. P. Vigier, Proceedings of the Colston Research Society (1957).
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  4. P. Hillion and J. P. Vigier, Annales de l'Institut H. Poincaré 16 (1959), 161.
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  12. T. Takabayasi, See ref. 1).
  13. F. Halbwachs, P. Hillion and J. P. Vigier, C. R. Acad. Sc. 250 (1960), 471.
  14. F. Halbwachs, P. Hillion and J. P. Vigier, Nuovo Cim. 15 (1960), 209.
  15. P. Hillion and J. P. Vigier, Quantification du mouvement interne des masses fluides relativistes seminaires L. de Broglie, Ed. Revue d'optique (1959).
  16. P. Hillion and J. P. Vigier, Nucl. Phys. 16 (1960), 360[Elsevier].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 29 No. 2 (1963) pp. 279-295 :
    A Theory of Elementary Particles with Internal Degrees of Freedom
    Haruo Shimazu and Kan-ichi Yokoyama
  2. Progress of Theoretical Physics Vol. 32 No. 6 (1964) pp. 940-949 :
    The Rotator Theory of Elementary Particles and the Baryon Masses
    F. Halbwachs

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