Recently two variational strategies have been applied to the standard and linear $\delta$ expansions for quantum field theories. These strategies, both of which improve the accuracy of the expansions, have the property that for $N$ self-interacting fields at large $N$ the lowest-order $\delta$ expansion improved by the variational strategy gives the exact large-$N$ result. In this article, we study, in the context of supersymmetric quantum mechanics, the numerical accuracy of the improved $\delta$ expansions when calculated to large order in $\delta$ and compare them with the accuracy of the large-$N$ expansion. We find that the usual $\delta$ expansion is the most accurate, followed by the linear $\delta$ expansion. The large-$N$ expansion, analytically continued to $N=1\mathrm{}$, is the least accurate method of the three.

• Received 31 January 1991

DOI:https://doi.org/10.1103/PhysRevD.43.3396