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


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.


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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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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