Quantum geometry and resurgent perturbative/nonperturbative relations

Gerald Dunne
Certain quantum spectral problems have the remarkable property that the formal perturbative series for the energy spectrum can be used to generate all other terms in the entire trans-series, in a completely constructive manner. I explain a geometric all-orders WKB approach to these perturbative/non-perturbative relations, which reveals surprising connections to number theory and modular forms.
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