New start for local composite operators

We present a formalism for local composite operators. The corresponding effective potential is unique, multiplicatively renormalizable; it is the sum of one-particle-irreducible diagrams and can be interpreted as an energy-density. First we apply this method to λφ⁴ theory, where we check renormalizability up to three loops, and second to the Coleman-Weinberg model, where gauge independence of the effective potential for the local composite operator φφ* is explicitly checked up to two loops.