Callan-Symanzik Equations andεExpansions

Abstract

We analyze a noncanonically renormalized ${\phi }^4$ theory in $4-\epsilon$ dimensions with the aid of normal-product methods. By a systematic use of Callan-Symanzik equations we show how a critical point can be determined and the anomalous scale dimensions of all composite operators obtained by using Wilson's $\epsilon$ expansion. These methods are also applied to the coefficient distributions appearing in operator-product expansions.