Seminario INFN di Gruppo IV

Perturbative series in quantum mechanics and quantum field theory are known to be only asymptotic and generically require the inclusion of extra contributions non-perturbative in the coupling, such as instantons, to reproduce exact results.
Using a geometrical approach based on the Picard-Lefschetz theory and Borel resummation methods, we show how exact results can be encoded in a modified perturbative series in a class of quantum mechanical systems. There is no need of transseries, i.e. non-perturbative effects, such as real (or complex) instantons.

Applications are presented and perspectives for quantum field theories are shortly discussed.