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The power of series

Gabriele Spada
SISSA Trieste
Tuesday, April 11, 2017 - 16:15

In quantum mechanics, perturbation theory around the harmonic oscillator eigenstates usually features factorially growing coefficients and hence does not converge. After giving an overview of Borel resummation I will show that the asymptotic series associated to a regular path of steepest descent (thimble) is Borel resummable to the exact result. Using a geometrical approach based on the Picard-Lefschetz theory I will then characterize the conditions under which the perturbative expansion of a quantum mechanical system leads to the full answer. When such conditions are not met, it is still possible to define a modified perturbative expansion that reproduces the full answer without the need non-perturbative contributions. Based on a recent work with Marco Serone and Giovanni Villadoro.

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