Effective action of a local composite operator

The general graph rule of the effective action Γ of a local composite operator is derived in a compact form. The inversion method is used to obtain the explicit form of Γ. With this rule the order parameter φ is changed to its conjugate variable ${\mathit{J}}^{\mathrm{}\left(0\right)\mathrm{}}$[φ] which appears in the lowest inversion relation. Throughout the discussion ${\mathit{J}}^{\mathrm{}\left(0\right)\mathrm{}}$[φ] plays an essential role. The use of the present method is illustrated by applying it to the gauge invariant study of the strong coupling phase of massless QED and positronium states.