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Il Nuovo Cimento A (1971-1996)

, Volume 45, Issue 3, pp 656–665 | Cite as

Vanishing renormalization constants and spontaneous generation of symmetries

  • S. A. Bludman
  • N. G. Deshpande
Article

Summary

Dynamical origin of symmetries in potential problems has recently received a great deal of attention. The purpose of this paper is to point out that there exists a soluble model in quantum field theory, namely the Ruijgrok-Van Hove model, where the solutions possess a higher symmetry than apparent in the original Hamiltonian. The symmetries arise due to the dynamics and are exact only in the limit of vanishing renormalization constants. Thus the model illustrates how the bootstrap principle applied to field theory can generate symmetries spontaneously. We also point out the role played by inequivalent transformation in symmetry generation as is the case in the spontaneous symmetry breakdown.

Riassunto

Recentemente l'origine dinamica delle simmetrie nei problemi di potenziale ha attirato molto l'attenzione. Scopo di questo articolo è di far notare che nella teoria quantistica dei campi esiste un modello risolvibile, cioè il modello di Ruijgrok-Van Hove le cui soluzioni possiedono una maggior simmetria di quella che compare nell'hamil toniano originario. Le simmetrie sono effetto della dinamica e sono esatte solo quando le costanti di rinormalizzazione tendono a zero. Così il modello illustra come il principio di bootstrap applicato alla teoria dei campi può generare spontaneamente simmetrie. Si mette in rilievo anche il ruolo ricoperto dalla trasformazione inequivalente nell generazione di simmetrie come è il caso nella rottura spontanea della simmetria.

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Copyright information

© Società Italiana di Fisica 1966

Authors and Affiliations

  • S. A. Bludman
    • 1
  • N. G. Deshpande
    • 2
  1. 1.Department of PhysicsUniversity of PennsylvaniaPhiladelphia
  2. 2.Institute of Mathematical SciencesMadras

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