Large Field Cutoffs Make Perturbative Series Converge

For lambda phi^4 problems, convergent perturbative series can be obtained by cutting off the large field configurations. The modified series converge to values exponentially close to the exact ones. For lambda larger than some critical value, the method outperforms Pade approximants and Borel summations. We discuss some aspects of the semi-classical methods used to calculate the modified Feynman rules and estimate the error associated with the procedure. We provide a simple numerical example where the procedure works despite the fact that the Borel sum has singularities on the positive real axis.