Il Nuovo Cimento A (1965-1970)

, Volume 55, Issue 1, pp 110–124 | Cite as

On the wigner coefficients of the three-dimensional Lorentz group

  • I. Ferretti
  • M. Verde
Article
First Online:
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Summary

The Lorentz group in three dimensionsL3 is the Wigner little group corresponding to spacelike momenta. In this paper an explicit calculation of the 3-j coefficients ofL3 is made. Their behaviour under interchanging or changing of signs of the five independent parameters which identify them has been also investigated. The method used is of some interest since it is in principle susceptible of extending toL3 all the Racah algebra familiar from the three-dimensional rotation group.

Keywords

Discrete Spectrum LORENTZ Group Rotational Angular Momentum Manuscript Project Positive Half Axis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

О коэффицнентах Вигнера для трехмерной группы Лорентца

Резюме

Трехмерная группа ЛорентцаL3 представляет маленькую вигиеровскую группу, соответствующую пространственно-подобному импульсу. В этой статье проводится точное вычисление 3-j коэффициентов дляL3. Гыло также исследовано их поведение при перемешивании или измеменении знаков пяти независимых параметров, которые характеризуют эти коэффицициенты. Использованный метод в случае группыL3; в принципе, может быть использован для вывода полной алгебры Рака, хорошо известной для группы вращения в трехмерном пространстве.

Riassunto

Il gruppo di Lorentz a tre dimensioniL3 è il piccolo gruppo degli impulsi di tipo spazio. In questo lavoro si presenta il calcolo esplicito dei coefficienti 3-j diL3 assieme ad uno studio delle proprietà di simmetria dei coefficienti 3-j rispetto a permutazioni od inversioni di segno dei cinque parametri indipendenti che li caratterizzano. Il metodo che si usa può essere in linea di principio esteso a derivare l’intera algebra di Racah, ben nota per il gruppo delle rotazioni in tre dimensioni, al caso del gruppoL3.

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References

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Copyright information

© Società Italiana di Fisica 1968

Authors and Affiliations

  • I. Ferretti
    • 1
  • M. Verde
    • 1
  1. 1.Istituto di Fisica Teorica dell’UniversitàTorino

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