Aspects of Resurgence

Jeriek Van den Abeele, FI

Given that physical problems rarely have exact solutions, the importance of perturbation theory can hardly be overstated. Yet often, a closer look reveals that it is divergent and ill-defined! Non-perturbative effects, ubiquitous in nature and quantum theories, have to be accounted for explicitly in attempts to make sense of perturbation theory. The perspective of the resurgence framework leads to new ways of understanding perturbative expansions and reveals surprising connections to non-perturbative physics. In this talk, I will illustrate how resurgence manifests itself in the quantum mechanical context of a cosine potential, emphasising the importance of quantum tunnelling for its energy spectrum and highlighting how non-perturbative contributions are intricately encoded in perturbation theory.

(The slides will be available here)