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Résumé |
In quantum theory, we often calculate observables approximately by using
perturbative series in a small parameter. These series are typically factorially
divergent,
so we need to make sense of them. The theory of resurgence
gives a general framework to do this, and upgrades perturbative series to so-
called
trans-series, which include exponentially small corrections and make it possible
to incorporate
non-perturbative physics in a systematic way. Many non-perturbative
techniques in quantum theory (like instanton calculus and renormalon physics) are
in fact particular examples
of this general framework. In these lectures I will give an introduction to
resurgence with a focus on applications
to quantum theory. After introducing some elementary resurgent technology, I will
discuss resurgence
in one-dimensional quantum mechanics, and then proceed to discuss what is known
about the resurgent structure
of quantum field theory. |
