A new perturbative approach for the anharmonic oscillator

A new perturbative approach is presented and applied to the anharmonic oscillator. Estimating the large-order behaviour by means of the Lipatov method, the new perturbation expansion turns out to be convergent for the partition function at non-zero temperature. Although the new perturbation expansion is not convergent for the ground-state energy, it nevertheless provides accurate approximations, even in situations which cannot be treated by standard perturbation techniques, like the strong coupling regime.