The Power of Series


Villadoro, G. (2017). The Power of Series. Perimeter Institute. https://pirsa.org/17090055


Villadoro, Giovanni. The Power of Series. Perimeter Institute, Sep. 12, 2017, https://pirsa.org/17090055


          @misc{ pirsa_PIRSA:17090055,
            doi = {10.48660/17090055},
            url = {https://pirsa.org/17090055},
            author = {Villadoro, Giovanni},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {The Power of Series},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {sep},
            note = {PIRSA:17090055 see, \url{https://pirsa.org}}

Giovanni Villadoro The Abdus Salam International Centre for Theoretical Physics (ICTP)


After a small review on divergent series and Borel resummation I will discuss a geometric approach based on Picard-Lefschetz theory to study the interplay between perturbative and non-perturbative effects in the QM path integral.

Such approach 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 show how a simple deformation of the original perturbation theory allows to recover the full non perturbative answer from the perturbative coefficients alone, without the need of including instanton corrections. I will illustrate this technique in examples which are known to contain non-perturbative effects, such as the (supersymmetric) double-well potential, the pure anharmonic oscillator, and the perturbative expansion around a false vacuum.