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Résumé |
After a short review on divergent series and Borel resummation I will discuss a geometric approach based on Picard-Lefschetz theory which can be used to characterize when the perturbative series gives the full answer and when the inclusion of non-trivial saddles--instantons is mandatory. I will then consider the \lambda \phi^4 model in one and two dimensions and show that by resummation of the perturbative series it ispossible to extract some non-perturbative information, such as the non-perturbative level splitting in the quantum mechanical double well and the critical parameters at the phase transition in the quantum field theory case. |
