Advertisement

Il Nuovo Cimento A (1965-1970)

, Volume 53, Issue 1, pp 201–212 | Cite as

Nonexistence of classes of Yang-Mills fields

  • H. G. Loos
Article

Summary

Nonexistence is shown for regular localized free classical Yang-Mills fields with nonvanishingϕ α , with a semi-simple and compact internal holonomy group, and with one of the following types of time dependence: 1) there exists a gauge in which the potentials are independent of time, 2) the gauge fieldϕ ϰλ is covariant constant in time, 3) there exists an internal operator fieldT(x ϰ ) such that ∇ t ϕ ϰλ =[T,ϕ ϰλ ] where ∇ ϰ T belongs to the Lie algebra of the holonomy group, and the matrix formed from the adjoint representation of the gauge field and its dual has maximal rank.

Keywords

Gauge Transformation Gauge Field Event Space Holonomy Group Covariant Constant 
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.

Отсутвие классов для полей Янга-Миллса

Резюме

Показывается отсутствие для регулярных локализованных свободных классических полей Янга-Миллса с неисчезающимϕ , с полупротой и компактной внешней голономиой группой и с одним из следующих типов временной зависимости: 1) существует калибровка, в которой потенциалы не зависят от времени, 2) калибровочное полеϕ ϰλ является постоянным во времени 3) существует внешнее операторное полеT(x ϰ ), такое, что ∇ t ϕ ϰλ =[T,ϕ ϰλ , где ∇ ϰ T принадлежит алгебре Ли голономной группы, и матрица, образованная из сопряженного представления калибровочного поля и его дуала, имеет максимальный ранг.

Riassunto

Si dimostra la non esistenza di campi classici di Yang-Mills liberi, localizzati e regolari conϕ non nullo, con un gruppo di olonomie interne compatto e semisemplice; e con uno dei seguenti tipi di dipendenza dal tempo: 1) esiste un gauge in cui i potenziali sono indipendenti dal tempo, 2) il campo di gaugeϕ ϰλ è covariante, costante nel tempo, 3) esiste un campo interno di operatoriT(x ϰ ) tale che ∇ϕ ϰλ =[T,ϕ ϰλ , dove ∇ ϰ T appartiene all'algebra di Lie del gruppo di olonomia e la matrice formata dalla rappresentazione aggiunta del campo di gauge e del suo duale ha il massimo rango.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    C. N. Yang andR. L. Mills:Phys. Rev.,96, 191 (1954).ADSMathSciNetCrossRefGoogle Scholar
  2. (2).
    H. G. Loos:Nucl. Phys.,72, 677 (1965).MathSciNetCrossRefGoogle Scholar
  3. (3).
    H. G. Loos:Ann. of Phys.,36, 486 (1966).ADSMathSciNetCrossRefGoogle Scholar
  4. (4).
    R. P. Treat:Nuovo Cimento,50 A, 871 (1967).ADSCrossRefGoogle Scholar
  5. (5).
    J. Schwinger:Elementary Particles and High-Energy Physics, 1963Cargèse Summer School for Theoretical Physics (New York, 1965), p. 272.Google Scholar
  6. (6).
    J. Schwinger:Phys. Rev.,125, 1043 (1962).ADSMathSciNetCrossRefGoogle Scholar
  7. (7).
    S. I. Fickler: Dissertation Syracuse University (1961).Google Scholar
  8. (8).
    R. L. Arnowitt andS. I. Fickler:Phys. Rev.,127, 1821 (1962).ADSMathSciNetCrossRefGoogle Scholar
  9. (9).
    H. G. Loos:Journ. Math. Phys., September 1967.Google Scholar
  10. (10).
    A. Nyenhuis:Koninkl. Akad. Wetenschap. Amsterdam, Proceedings A57, No. 1, 17 (1954).Google Scholar
  11. (14).
    H. G. Loos:Nuovo Cimento,52 A, 1085 (1967).ADSCrossRefGoogle Scholar
  12. (15).
    M. Ikeda andY. Myachi:Progr. Theor. Phys.,27, 474 (1962).ADSCrossRefGoogle Scholar
  13. (16).
    H. G. Loos:Journ. Math. Phys., August 1967.Google Scholar
  14. (17).
    This scalar product is proportional to the scalar product defined in the Lie algebra by the group metric.Google Scholar
  15. (18).
    An index occurring between vertical lines does not participate in the alternation.Google Scholar
  16. (19).
    H. G. Loos:Ann. of Phys.,25, 91 (1963).ADSMathSciNetCrossRefGoogle Scholar
  17. (20).
    R. P. Treat: private communication.Google Scholar

Copyright information

© Società Italiana di Fisica 1968

Authors and Affiliations

  • H. G. Loos
    • 1
    • 2
  1. 1.Douglas Advanced Research LaboratoriesHuntington Beach
  2. 2.University of CaliforniaRiverside

Personalised recommendations