Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-10-06
Phys.Rev.D49:4219-4225,1994
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, LaTeX, Imperial/TP/92-93/55
Scientific paper
10.1103/PhysRevD.49.4219
Recent proofs of the convergence of the linear delta expansion in zero and in one dimensions have been limited to the analogue of the vacuum generating functional in field theory. In zero dimensions it was shown that with an appropriate, $N$-dependent, choice of an optimizing parameter $\l$, which is an important feature of the method, the sequence of approximants $Z_N$ tends to $Z$ with an error proportional to ${\rm e}^{-cN}$. In the present paper we establish the convergence of the linear delta expansion for the connected vacuum function $W=\ln Z$. We show that with the same choice of $\l$ the corresponding sequence $W_N$ tends to $W$ with an error proportional to ${\rm e}^{-c\sqrt N}$. The rate of convergence of the latter sequence is governed by the positions of the zeros of $Z_N$.
Bender Carl M.
Duncan Alan
Jones Hugh F.
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