Linked diagram theorem for effective interaction

We revisit the so-called linked diagram theorem for the effective interaction in open systems. First, we outline a novel proof of the linked diagram theorem, which is much simpler than the existing proof and leads naturally to a new form of the theorem. Second, we show that the linked diagram theorem in its known form gives many redundant diagrams which cancel among themselves in the exact perturbation expansion, while the new form is free of such redundant diagrams. At the end, we point out that all existing microscopic effective interactions suffer from such redundant contributions, and outline the way out of such difficulties. (author)