Il Nuovo Cimento B (1971-1996)

, Volume 20, Issue 2, pp 309–325 | Cite as

Solutions of the Dirac equation in finite de Sitter space (representations ofSO4.1)

  • F. Riordan


All the solutions of the Dirac equation in the finite space de Sitter universe are found and it is shown that they form a basis for a representation of the group of motions for this universe,SO4,1. The action of the generators ofSO4.1 on these solutions is explicitly given as a linear superposition of solutions.

Решения уравнения Дирака в конечном пространстве де Ситтера (представленияSO4,1)


Определяются все рещения уравнения Дирака в конечном пространстве вселенной де Ситтера. Показывается, что они образуют базис для представления группы движений для этой вселенной,SO4,1. В явном виде приводится действие генераторовSO4.1 на эти решения, в виде линейной суперпозиции решений.


Si trovano tutte le soluzioni delle equazioni di Dirac nell'universo di de Sitter dello spazio finito e si mostra che esse formano la baseSO4,1 per una rappresentazione del gruppo dei movimenti per questo universo. Su queste soluzioni si dà esplicitamente l'azione dei generatori diSO4,1 come sovrapposizione lineare delle soluzioni.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. (1).
    W. de Sitter:Month. Not.,78, 3 (1917).CrossRefMATHGoogle Scholar
  2. (2).
    Cf. ref. (7). andF. Gürsey:Istanbul Summer School 1962 (New York, N.Y., 1964);F. Gürsey andT. D. Lee:Proc. Nat. Acad. Sci.,49, 179 (1963).MathSciNetCrossRefGoogle Scholar
  3. (3).
    R. Herman:Comm. Math. Phys.,3, 53 (1966);M. Levy-Nahas:Journ. Math. Phys.,8, 211 (1967). The Poincaré group is a contraction (E. Inönü andE. P. Wigner:Proc. Nat. Acad. Sci.,39, 510 (1953)) of the de Sitter group.MathSciNetADSCrossRefMATHGoogle Scholar
  4. (4).
    W. Tait andJ. F. Cornwell:Journ. Math. Phys.,12, 1651 (1971).MathSciNetADSCrossRefGoogle Scholar
  5. (5).
    L. O'Raifeartaigh:Phys. Rev.,139, B 1052 (1965).MathSciNetADSCrossRefMATHGoogle Scholar
  6. (6).
    W. L. Bade andH. Jehle:Rev. Mod. Phys.,25, 714 (1953);P. G. Bergmann:Phys. Rev.,107, 624 (1957);D. R. Brill andJ. A. Wheeler:Rev. Mod. Phys.,29, 465 (1957);S. Weinberg:Gravitation and Cosmology, Chap. 12, Sect.5 (New York, N. Y., 1972).MathSciNetADSCrossRefGoogle Scholar
  7. (7).
    P. A. M. Dirac:Ann. of Math.,36, 657 (1935).MathSciNetCrossRefMATHGoogle Scholar
  8. (8).
    Summations over repeated indices are implied throughout this paper except in (A.18)–(A.20) μ=1, 2, 3, 4 andx 4 is imaginary.a, b=1, 2, 3, 4, 5;i,j=1, 2, 3, 5.Google Scholar
  9. (9).
    Cf. for exampleL. C. Biedenharn:Journ. Math. Phys.,2, 434 (1961).MathSciNetADSCrossRefGoogle Scholar
  10. (10).
    Cf. for exampleF. Riordan:Nuovo Cimento,16 A, 529 (1973), Appendix B.MathSciNetADSCrossRefGoogle Scholar
  11. (11).
    Cf. for exampleM. Abramowitz andI. A. Stegun:Handbook of Mathematical Functions, equations (8.5.2) and (8.6.6).Google Scholar

Copyright information

© Società Italiana di Fisica 1974

Authors and Affiliations

  • F. Riordan
    • 1
  1. 1.University of BirminghamBirmingham

Personalised recommendations