Abstract
When one tries to compute large orders in the 1/N series “à la Lipatov” a complicated non-linear equation for the instanton is found in ø4 or non-linear sigma models.
We solve here this equation in the one-dimensional case (quantum mechanics) by inverse scattering techniques. From the instanton solutions we obtain theK th order of the 1/N perturbation theory up to 0(K −1) for the 0(N) symmetric anharmonic oscillator and up to a factor 0(K 0) for a non-symmetric model. In the symmetric case we agree with results recently obtained in quantum mechanics by Hikami and Brézin following a different procedure. For the non-symmetric anharmonic oscillator we believe our formulae are new.
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References
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Communicated by E. Brézin
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de Vega, H.J. Large orders in the 1/N perturbation theory by inverse scattering in one dimension. Commun.Math. Phys. 70, 29–42 (1979). https://doi.org/10.1007/BF01220500
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DOI: https://doi.org/10.1007/BF01220500