Advertisement

Il Nuovo Cimento A (1965-1970)

, Volume 52, Issue 1, pp 242–254 | Cite as

Conserved currents, renormalization and zero-mass states

  • J. A. Swieca
Article

Summary

It is shown that charge renormalization corresponds to a form of a spontaneous symmetry breakdown: although the charge operator exists, it can no longer be written as a space integral of the, charge density. This can only happen due to the presence of zero-mass states in the theory, in full agreement with recent results on continuous symmetry groups in relativistic field theories.

Keywords

Local Operator Relativistic Field Theory Charge Operator Massive Vector Meson Charge Renormalization 
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.

Сохраняющиеся токи, перенормировка и состояния с нулевой массой

Резюме

Показывается, что перенормировка заряда соответствует форме спонтанного нарушения симметрии: хотя оператор заряда существует, но он не может больше быть записан, как пространственный интеграл от плотности заряда. Это может произойти только из-за наличия состояний с нулевой массой в теории, что находится в полном согласии с недавними результатами в непрерывных группах симметрий в релятивистских теориях поля.

Riassunto

Si fa vedere come la rinormalizzazione di carica corrisponde ad una forma di rottura spontanea della simmetria: sebbene l’operatore di carica esista, non può essere ancora scritto come un integrale spaziale della densità di carica. Questo può accadere solo per la presenza nella teoria di stati di massa nulla, in pieno accordo coi recenti risultati sui gruppi continui di simmetria ottenuti nelle teorie di campo relativistiche.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    D. Kastler, D. Robinson andJ. A. Swieca:Commun. Math. Phys.,2, 108 (1966).ADSMathSciNetCrossRefGoogle Scholar
  2. (2).
    B. Schroer andP. Stichel:Commun. Math. Phys.,3, 208 (1966).ADSMathSciNetCrossRefGoogle Scholar
  3. (3).
    J. A. Swieca:Phys. Rev. Lett.,17, 974 (1966).ADSMathSciNetCrossRefGoogle Scholar
  4. (4).
    J. Goldstone, A. Salam andS. Weinberg:Phys. Rev.,127, 965 (1962);Y. Nambu andG. Jona Lasinio:Phys. Rev.,122, 345 (1961);J. Goldstone:Nuovo Cimento,19, 154 (1961).ADSMathSciNetCrossRefGoogle Scholar
  5. (5).
    R. V. Lange:Phys. Rev. Lett.,14, 3 (1965).ADSCrossRefGoogle Scholar
  6. (6).
    G. S. Guralnik, T. Kibble andC. R. Hagen:Phys. Rev. Lett.,13, 585 (1964).ADSCrossRefGoogle Scholar
  7. (7).
    J. A. Swieca:Commun. Math. Phys.,4, 1 (1967).ADSMathSciNetCrossRefGoogle Scholar
  8. (8).
    H. Ezawa andJ. A. Swieca:Commun. Math. Phys.,5, 330 (1967).ADSMathSciNetCrossRefGoogle Scholar
  9. (9).
    R. Streater andA. Wightman:PCT, Spin, Statistics and All That (New York, 1964).Google Scholar
  10. (10).
    R. Haag:Phys. Rev., 112, 669 (1958).ADSMathSciNetCrossRefGoogle Scholar
  11. (11).
    D. Ruelle:Helv. Phys. Acta,35, 147 (1962).MathSciNetGoogle Scholar
  12. (12).
    R. P. Feynman andM. Gell-Mann:Phys. Rev.,109, 193 (1958).ADSMathSciNetCrossRefGoogle Scholar
  13. (13).
    K. Johnson:Nuovo Cimento,20, 773 (1961).CrossRefGoogle Scholar
  14. (14).
    J. C. Ward:Phys. Rev.,77, 293 (1950);Y. Takahashi:Nuovo Cimento,6, 370 (1957).ADSCrossRefGoogle Scholar
  15. (15).
    K. Bardakci, M. B. Halpern andG. Segré: preprint.Google Scholar
  16. (16).
    J. Schwinger:Phys. Rev.,76, 790 (1949).ADSMathSciNetCrossRefGoogle Scholar
  17. (17).
    G. Källen:Helv. Phys. Acta,25, 417 (1952);H. Lehmann:Nuovo Cimento,11, 342 (1954).Google Scholar
  18. (18).
    D. Pines:Elementary Excitations in Solids (New York, 1963).Google Scholar
  19. (19).
    H. Araki, K. Hepp andD. Ruelle:Helv. Phys. Acta,35, 164 (1962).MathSciNetGoogle Scholar

Copyright information

© Società Italiana di Fisica 1967

Authors and Affiliations

  • J. A. Swieca
    • 1
  1. 1.Department of PhysicsUniversity of São PauloSão PauloBrasil

Personalised recommendations