Communications in Mathematical Physics

, Volume 97, Issue 1–2, pp 211–225 | Cite as

Reduction in the number of coupling parameters

  • W. Zimmermann


A method is developed for reducing the formulation of massless models with several independent couplings to a description in terms of a single coupling parameter. The original as well as the reduced system are supposed to be renormalizable and invariant under the renormalization group. For most models there are, if any, only a finite number of reductions possible including those which correspond to symmetries of the system. The reduction method leads to a consistent formulation of the reduced model in any order of perturbation theory even in cases where it is difficult to establish a symmetry in higher orders. An example where no symmetry seems to be involved is the interaction of a spinor field with a pseudoscalar field. For this model the reduction method determines the quartic coupling constant uniquely as a function of the Yukawa coupling constant. The Wess-Zumino model is an exceptional case for which the reduction method admits an infinite number of solutions besides the supersymmetric one.


Neural Network Perturbation Theory Finite Number Renormalization Group Yukawa Coupling 
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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • W. Zimmermann
    • 1
  1. 1.Max-Planck-Institut für Physik und Astrophysik, Werner-Heisenberg-Institut für PhysikMünchen 40Federal Republic of Germany

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