HOW TO AVOID THE ASYMPTOTIC-EXPANSION

Treating the anharmonic part of the action as a collective variable reduces the problem of calculating the contribution of "large" fluctuations to the functional integral to that of calculating a simple integral. This method allows one to avoid the problem of the resummation of the perturbative asymptotic series, thus providing sensible results in non-Borel-summable cases. To improve the accuracy of the results, the contribution of "small" fluctuations can be corrected by a precise calculation of some low order perturbation theory terms. The ground state energy of an anharmonic oscillator is calculated in both Borel-summable and non-Borel-summable cases.