Geodesic
On the breakdown of perturbation theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 2, pp. 187-196

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The production of $\scriptstyle o({1\over g^2})$ particles in a weakly-coupled theory is believed to be non-perturbatively suppressed. I comment on the prospects of (a) establishing this rigorously, and (b) estimating the effect to exponential accuracy semiclassically, by discussing two closely-related problems: the large-order behaviour of few-point Green functions, and induced excitation in quantum mechanics. Induced tunneling in the latter case is exponentially enhanced for frequencies of the order of the barrier height. 
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     author = {C. Bachas},
     title = {On the breakdown of perturbation theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {187--196},
     publisher = {mathdoc},
     volume = {95},
     number = {2},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_95_2_a2/}
}
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C. Bachas. On the breakdown of perturbation theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 2, pp. 187-196. http://geodesic.mathdoc.fr/item/TMF_1993_95_2_a2/