COMPOSITENESS AND THE REDUCTION OF COUPLINGS

We study in lowest-order mean-field perturbation theory (the fermion loop approximation) the linear sigma-model in two and four dimensions described by the two couplings lambda and g. We examine the relations obtained by imposing the compositeness conditions Z3 = Z4 = 0 and those obtained by the strategy of trying to reduce the number of coupling constants by looking for a self-consistent solution of the renormalization-group equations for which lambda = f(g2). We find that the reduction-of-couplings strategy gives the same relationship between lambda and g2 as that found by imposing the compositeness conditions.