Abstract
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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Communicated by G. Mack
Dedicated to the memory of Kurt Symanzik
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Zimmermann, W. Reduction in the number of coupling parameters. Commun.Math. Phys. 97, 211–225 (1985). https://doi.org/10.1007/BF01206187
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DOI: https://doi.org/10.1007/BF01206187