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The groupF 4 and its generators

ГруппаF 4 и ее генераторы

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Il Nuovo Cimento B (1965-1970)

Summary

The representations ofF 4 are discussed and the decompositions of some representations in the reductionsSO 26 →F 4 →SO 9 are tabulated. The decompositions of some inner products ofF 4 are also tabulated. A general method of constructing operator bases for representations of larger groups is given. Using this method, operators corresponding to the generators ofF 4 acting on the representation (1000) are constructed. This method also generates relations between 6-j symbols and some examples are given.

Riassunto

Si discutono le rappresentazioni diF 4 e si tabulano le decomposizioni di alcune rappresentazioni nelle riduzioniSO 26 →F 4 →SO 9. Si tabulano anche le decomposizioni di alcuni prodotti interni diF 4. Si dà un metodo generale per costruire basi di operatori per rappresentazioni di gruppi maggiori. Usando questo metodo si costruiscono operatori corrispondenti ai generatori diF 4 agenti sulla rappresentazione (1000). Con questo metodo si generano anche relazioni fra i simboli 6-j; si forniscono alcuni esempi.

Реэюме

Обсуждаются представленияF 4, и табулируются раэложения некоторых представлений в преобраэованияхSO 26 →F 4 →SO 9. Также табулируются раэложения некоторых внутренних проиэведений группыF 4. Приводится обший метод конструирования операторных баэисов для представлений больщих груии. Испольэуя зтот метод, конструируются операторы, соответствуюшие генераторамF 4, действуюшим на представление (1000). Этот метод также обраэует соотнощение между 6-j символами, и приводятся некоторые примеры.

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References

  1. E. Cartan: Thèse, Paris (1894).

  2. H. Weyl:Theory of Groups and Quantum Mechanics, Translated from German (New York, 1950).

  3. M. Hamermesh:Group Theory and Its Application to Physical Problems (Reading, Mass., 1962).

  4. B. R. Judd:Operator Techniques in Atomic Spectroscopy (New York, 1963).

  5. G. Racah:Rev. Mod. Phys.,76, 1352 (1949).

    Article  MathSciNet  Google Scholar 

  6. The group-theoretical methods used can be found in Chap. 5 of the book byJudd (4), inR. E. Behrends, S. Dreitlein, C. Fronsdal andW. Lee:Rev. Mod. Phys.,34, 1 (1962), or inG. Racah:Princeton Lecture Notes (unpublished).

  7. H. Weyl:Math. Zeits.,23, 271 (1925);24, 328, 377 (1925).

    Article  MathSciNet  Google Scholar 

  8. E. Cartan:Bull. Soc. Math. de France,41, 53 (1913).

    MathSciNet  Google Scholar 

  9. B. R. Judd andH. T. Wadzinski:Journ. Math. Phys.,8, 2125 (1967).

    Article  ADS  Google Scholar 

  10. A. R. Edmonds:Angular Momentum in Quantum Mechanics (Princeton, 1957).

  11. M. Rotenberg, N. Metropolis, R. Bivens andJ. K. Wooten:The 3-j and 6-j Symbols (Cambridge, Mass., 1959).

  12. J. P. Elliott:Proc. Roy. Soc., A201, 516 (1956).

    Google Scholar 

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Authors and Affiliations

  1. Physics Department, The Johns Hopkins University, Baltimore, Md.

    H. T. Wadzinski

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  1. H. T. Wadzinski
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Wadzinski, H.T. The groupF 4 and its generators. Nuovo Cimento B (1965-1970) 62, 247–257 (1969). https://doi.org/10.1007/BF02710135

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  • DOI: https://doi.org/10.1007/BF02710135

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