2 research outputs found
Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions
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, -dependent, choice of an optimizing parameter \l, which is an
important feature of the method, the sequence of approximants tends to
with an error proportional to . In the present paper we
establish the convergence of the linear delta expansion for the connected
vacuum function . We show that with the same choice of \l the
corresponding sequence tends to with an error proportional to . The rate of convergence of the latter sequence is governed by
the positions of the zeros of .Comment: 20 pages, LaTeX, Imperial/TP/92-93/5
On the Divergence of Perturbation Theory. Steps Towards a Convergent Series
The mechanism underlying the divergence of perturbation theory is exposed.
This is done through a detailed study of the violation of the hypothesis of the
Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum
Field Theory. That theorem governs the validity (or lack of it) of the formal
manipulations done to generate the perturbative series in the functional
integral formalism. The aspects of the perturbative series that need to be
modified to obtain a convergent series are presented. Useful tools for a
practical implementation of these modifications are developed. Some resummation
methods are analyzed in the light of the above mentioned mechanism.Comment: 42 pages, Latex, 4 figure