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Il Nuovo Cimento A (1965-1970)

, Volume 17, Issue 1, pp 171–188 | Cite as

Properties of the Green’s functions under finite transformations of a soft-broken-symmetry group

  • R. Nobili
Article

Summary

In this paper transformation properties of Green’s functions are studied when, under rather general hypotheses, the local fields are subjected to finite transformations of a continuous group of soft broken symmetries. A perturbative series is found and its convergence conditions are discussed. Also the limiting case of spontaneously broken symmetries is considered to complete the picture. As an application transformation properties of Green’s functions under the dilatation group are considered. Finally a method is given to represent a general Green’s function as an expansion in series of dilatation-invariant terms; the related mathematical difficulties are also discussed.

Riassunto

In questo lavoro si studiano le proprietà di trasformazione delle funzioni di Green quando, entro ipotesi piuttosto generali, i campi locali sono soggetti a trasformazioni finite di un gruppo continuo di simmetrie rotte «mollemente». Si trova una serie perturbativa di cui si discutono le condizioni di convergenza. Per completare il quadro si tratta pure il caso delle rotture spontanee di simmetrie. Come applicazione si considerano le proprietà di trasformazione delle funzioni di Green rispetto al gruppo delle dilatazioni. Infine si dà un metodo per rappresentare una funzione di Green generale come sviluppo in serie di termini invarianti di scala; se ne discutono le difficoltà matematiche.

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References

  1. (1).
    H. Weyl:The Theory of Groups and Quantum Mechanics (New York).Google Scholar
  2. (2).
    M. Gell-Mann andY. Ne’eman:The Eightfold Way (New York, 1964);F. Y. Dyson:Symmetry Groups in Nuclear and Particle Physics (New York, 1965).Google Scholar
  3. (3).
    T. W. B. Kibble, D. Kastler andH.-P. Dürr inProceedings of the Rochester Conference (1967).Google Scholar
  4. (4).
    G. G. Amch:Algebraic Methods in Statistical Mechanics and Quantum Field Theory (New York, 1972);J. Dixmier:Les C *-algèbres et leurs représentation (Paris, 1969).Google Scholar
  5. (5).
    D. W. Robinson:Algebraic Aspects of Relativistic Quantum Field Theory, Proceedings of the Brandeis University of Summer School (New York, 1965), p. 389.Google Scholar
  6. (6).
    R. F. Streater andA. S. Wightman:P.C.T., Spin, Statistics, and All That (New York, 1964).Google Scholar
  7. (7).
    G. Mack andA. Salam:Ann. of Phys.,53, 174 (1969).MathSciNetCrossRefADSGoogle Scholar
  8. (8).
    S. Fubini, G. Furlan andC. Rossetti:Nuovo Cimento,40 A, 1171 (1965).MathSciNetCrossRefADSGoogle Scholar
  9. (9).
    L. P. Eisenhart:Continuous Groups of Transformations (New York).Google Scholar
  10. (10).
    H. J. Borchers, R. Hag andR. Schroer:Nuovo Cimento,29, 148 (1963).MATHCrossRefGoogle Scholar
  11. (11).
    R. F. Streater:Broken symmetries and the Goldstone theorem, inHigh-Energy Physics and Elementary Particles (Vienna, 1965).Google Scholar
  12. (12).
    J. Goldstone:Nuovo Cimento,19, 154 (1961).MathSciNetCrossRefGoogle Scholar
  13. (13).
    S. Ciccariello, R. Gatto, G. Sartori andM. Tonin:Ann. of Phys.,65, 265 (1971).MathSciNetCrossRefADSGoogle Scholar
  14. (14).
    B. W. Lee:Nucl. Phys.,9 B, 649 (1969).CrossRefADSGoogle Scholar
  15. (15).
    G. S. Guralnick:Phys. Rev.,136, B 1404, B 1417 (1964).MathSciNetCrossRefADSGoogle Scholar
  16. (16).
    D. Kastler:Proceedings of the Rochester Conference (New York, 1967).Google Scholar
  17. (17).
    C. G. Callan, S. Coleman andR. Jackiw:Ann. of Phys.,59, 42 (1970).MATHMathSciNetCrossRefADSGoogle Scholar

Copyright information

© Società Italiana di Fisica 1973

Authors and Affiliations

  • R. Nobili
    • 1
    • 2
  1. 1.Istituto di Fisica dell’UniversitàPadova
  2. 2.Istituto Nazionale di Fisica NucleareSezione di PadovaPadovaItalia

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