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Lettere al Nuovo Cimento (1971-1985)

, Volume 15, Issue 2, pp 39–40 | Cite as

Fallacy of perturbative methods for higher-spin equations

  • G. Velo
  • D. Zwanziger
Article
  • 31 Downloads

References

  1. (1).
    J. D. Kimel andL. M. Nath:Phys. Rev. D,6, 2132 (1972).ADSCrossRefGoogle Scholar
  2. (2).
    An existence proof for the Green’s function of the external-field Rarita-Schwinger equation is obviously very desirable, but does not seem to be attempted in the literature. The excellent review article:A. S. Wightman:Relativistic wave equations as singular hyperbolic systems, inProceedings of Symposia in Pure Mathematics, Vol.23, edited byD. C. Spencer, American Mathematical Society, reports on what mathematical results are at hand. The methods used in ref. (3–5)G. Velo andD. Zwanziger:Phys. Rev.,186, 1337 (1969).G. Velo:Nucl. Phys.,43 B, 389 (1972).G. Velo andD. Zwanziger: inLectures from the Coral Gables Conference on Fundamental Interactions at High Energy, Vol.4, edited byM. Dal Cin, G. J. Iverson andA. Perlmutter (New York, N. Y., London, and Paris, 1971), p. 8;G. Velo:Lett. Nuovo Cimento,3, 80 (1972);A. Shamaly andA. Z. Capri:Lett. Nuovo Cimento,3, 467, 637 (1972), give properties of the solutions, assuming their existence. If, contrary to our expectations, no solutions exist, the fallacy of perturbative methods is clear.Google Scholar
  3. (3).
    G. Velo andD. Zwanziger:Phys. Rev.,186, 1337 (1969).ADSCrossRefGoogle Scholar
  4. (4).
    G. Velo:Nucl. Phys.,43 B, 389 (1972).ADSCrossRefGoogle Scholar
  5. (5).
    G. Velo andD. Zwanziger: inLectures from the Coral Gables Conference on Fundamental Interactions at High Energy, Vol.4, edited byM. Dal Cin, G. J. Iverson andA. Perlmutter (New York, N. Y., London, and Paris, 1971), p. 8;G. Velo:Lett. Nuovo Cimento,3, 80 (1972);A. Shamaly andA. Z. Capri:Lett. Nuovo Cimento,3, 467, 637 (1972).Google Scholar
  6. (6).
    The early work ofK. Johnson andE. C. G. Sudarshan:Ann. of Phys.,13, 126 (1961) showed that a contradiction with positivity occurs using the Schwinger quantization procedure. The contradiction is understood when it is realized that this procedure correctly gives the equal-time commutator only on planes that lie outside the characteristic cone of the coupled Rarita-Schwinger equation. Since this cone lies in part outside the light-cone, this does not include all spacelike planes.MathSciNetADSCrossRefGoogle Scholar
  7. (7).
    P. C. Aichelburg, G. Ecker andR. U. Sexl:Nuovo Cimento,2 B, 63 (1971) propose to drop the external-field approximation and to introduce radiation reaction. Although this may well change the nature of the solution radically, this problem, by its very complication, raises a host of new difficulties, more than it provides a resolution of the old ones.ADSCrossRefGoogle Scholar
  8. (8).
    Theβ µ used here are given byβ µ =m B -1 Γ µ in the notations of ref. (2)Google Scholar

Copyright information

© Societàa Italiana di Fisica 1976

Authors and Affiliations

  • G. Velo
    • 1
  • D. Zwanziger
    • 1
  1. 1.Department of PhysicsNew York UniversityNew York

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