量子論における摂動展開と非摂動量子効果の不思議な関係 ~Resurgence 展開と複合ソリトン配位~

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  • リョウシロン ニ オケル セツドウ テンカイ ト ヒセツドウ リョウシ コウカ ノ フシギ ナ カンケイ : Resurgence テンカイ ト フクゴウ ソリトン ハイイ
  • Relation between perturbative and instanton calculations in quantum theories

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説明

The purpose of this work is to investigate the relation between perturbative calculation and non-perturbative physics in quantum theory. For this purpose, we calculate multi-instanton amplitudes in Sine-Gordon quantum mechanics by integrating out quasi-moduli parameters corresponding to separations of instantons and antiinstantons. We propose a proper extension of the prescription of Bogomolny and Zinn-Justin for multiinstanton configurations and the appropriate subtraction scheme. We obtain the multi-instanton contributions to the energy eigenvalue of the lowest band at the zeroth order of the coupling constant. For those with both instantons and anti-instantons, we obtain results with imaginary and ambiguous parts depending on the path of analytic continuation. We show that the imaginary parts of multi-instanton amplitudes precisely cancel the imaginary parts of the Borel resummation of the perturbation series. This result supports the conjectured resurgence structure, in which the combination of perturbative and instanton calculations could lead to a novel definition of the quantum theories including quantum field theory.

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