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SUMMARY:Borel Resummation in Exact Perturbation Theory and the Exact WKB M
ethod
DTSTART;VALUE=DATE-TIME:20230224T130000Z
DTEND;VALUE=DATE-TIME:20230224T140000Z
DTSTAMP;VALUE=DATE-TIME:20230321T052400Z
UID:indico-event-9347@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nikita Nikolaev\n\nI will present recent progress in
the amazing newly emerging subject of exact perturbation theory. This the
ory provides methods to upgrade divergent perturbative expansions to analy
tic information. One such method is called Borel resummation: it involves
a detailed analysis (via a Borel transform) of a given divergent perturbat
ive expansion in order to recover the nonperturbative corrections (i.e.\,
exponentially small terms) that otherwise cannot be captured by the ordina
ry perturbation theory. The astounding big-picture upshot of this theory i
s that — contrary to Freeman Dyson’s conclusion that perturbation theo
ry is incomplete — the divergent sector of perturbation theory actually
already encodes all the necessary nonperturbative information\, and it is
therefore only a matter of applying suitable methods to extract it.One of
the most classical settings for exact perturbation theory is the so-called
exact WKB method for solving singularly perturbed linear ODEs such as the
Schrödinger equation. Such ODEs can be easily solved in (exponential) po
wer series (the so-called WKB ansatz)\, but they are almost always diverge
nt. Attempting to apply Borel resummation to get true analytic solutions t
urns out to be the correct approach\, but a difficult mathematical problem
. I will describe a solution I have developed through a series of recent w
orks.\n\nhttps://indico.math.cnrs.fr/event/9347/
LOCATION:Fokko du Cloux (Bâtiment Braconnier)
URL:https://indico.math.cnrs.fr/event/9347/
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