Dependence of variational perturbation expansions on strong-coupling behavior: Inapplicability ofδexpansion to field theory

We show that in applications of variational theory to quantum field theory it is essential to account for the correct Wegner exponent ω governing the approach to the strong coupling, or scaling, limit. Otherwise the procedure does not converge at all or to the wrong limit. This casts doubt on all papers applying the so-called δ expansion to quantum field theory.