Geodesic
Asymptotic estimates in perturbation theory and the structure of functional integrals
Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 2, pp. 163-176 Cet article a éte moissonné depuis la source Math-Net.Ru

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The asymptotic series of perturbation theory are investigated for the example of the perturbation series for the ground-state energy of an anharmonic oscillator. The functional integrals in the Feynman expression for the ground-state energy are continued to the plane of complex values of the coupling constant $g$. The discontinuity of the functional integral across the cut $g\leqslant 0$ is calculated by the method of stationary phase. Because the extremals of the action are complex at unphysical values of $g$, the question arises of a transition in the functional integrals to integration with respect to a complex functional variable. By a special change of variable in the functional integral, this problem is reduced to the investigation of an ordinary integral. 
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M. Z. Iofa; D. Yu. Kuznetsov. Asymptotic estimates in perturbation theory and the structure of functional integrals. Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 2, pp. 163-176. http://geodesic.mathdoc.fr/item/TMF_1981_47_2_a1/

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