Departmental Bulletin Paper 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~
Relation between perturbative and instanton calculations in quantum theories

三角, 樹弘  ,  MISUMI, Tatsuhiro

36pp.15 - 25 , 2015-10-01 , 秋田大学大学院工学資源学研究科
The purpose of this work is to investigate the relation between perturbative calculation and non-perturbativephysics in quantum theory. For this purpose, we calculate multi-instanton amplitudes in Sine-Gordon quantummechanics 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 multiinstantonconfigurations and the appropriate subtraction scheme. We obtain the multi-instanton contributionsto the energy eigenvalue of the lowest band at the zeroth order of the coupling constant. For those with bothinstantons and anti-instantons, we obtain results with imaginary and ambiguous parts depending on the path ofanalytic continuation. We show that the imaginary parts of multi-instanton amplitudes precisely cancel theimaginary parts of the Borel resummation of the perturbation series. This result supports the conjecturedresurgence structure, in which the combination of perturbative and instanton calculations could lead to a noveldefinition of the quantum theories including quantum field theory.

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