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.


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© Springer-Verlag Berlin, Heidelberg 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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