Mikhail Kompaniets: Borel resummation of the asymptotic series
Almost all perturbative expansions in QFT are asymptotic series with factorially growing coefficients. Direct summation of such a series makes sense only for a small values of coupling constant and for relatively small orders of perturbative expansion (like in QED). To obtain physical estimates for such expansions for values of coupling constants that are not small, it is necessary to perform resummation of such a series. We will consider various resummation techniques based on the Borel transform and discuss their advantages/disadvantages and details of implementation.