CONVERGENCE OF THE OPTIMIZED DELTA-EXPANSION FOR THE CONNECTED VACUUMAMPLITUDE - ZERO DIMENSIONS

Recent proofs of the convergence of the linear delta expansion in zero and one dimension have been limited to the analogue of the vacuum gen erating functional in field theory. In zero dimensions it was shown th at with an appropriate, N-dependent, choice of an optimizing parameter lambda, which is an important feature of the method, the sequence of approximants Z(N) tends to Z with an error proportional to e(-cN). In the present paper we establish the convergence of the linear delta exp ansion for the connected vacuum function W = lnZ. We show that with th e same choice of lambda the corresponding sequence W(N) tends to W wit h an error proportional to e(-c square-root N). The rate of convergenc e of the latter sequence is governed by the positions of the zeros of Z(N).