# The Power of Series

### APA

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

### MLA

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

### BibTex

@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)

## Abstract

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.