Abstract
This paper presents an extension of Wilson's qualitative solution of the renormalization problem for the ${\ensuremath{\lambda}}_{0}{\ensuremath{\varphi}}^{6}$ interacting scalar field theory in one time and two space dimensions via renormalization-group recursion formulas. Specifically, we extend Wilson's qualitative derivation of renormalization-group recursion formulas to include the possibility of wave-function renormalization. We find that wave-function renormalization is indeed required for the interacting theory to be finite. As a consequence of wave-function renormalization, the field $\ensuremath{\varphi}$ has an anomalous dimension, about 0.53 in mass units.
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