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本文对近年来用微扰论来讨论散射振幅的解析性的理论,作了简单的介绍。在附录AⅠ中,计算了N-π,N-N散射的最简单图的奇异曲面上各点的相应临界αc,证实了除了在谱函数边界上的点外,临界αc都不落在实轴的(0,1)段中。在附录以AⅡ中,提出了色散关系的一个不受动量输送限制的证明方法。方法为对介子动量的方位角(讨论时取Breit系,核子动量取为极轴)进行平均。在附录AⅢ中,提出了一个可以带来么正条件的式子,以便在用微扰论进行对解析性的研究时考虑到么正条件。A short review on recent works on the analytic properties of perturbation expansions including those of Tarski, Eden is given. In the appendix, a number of related problems are discussed. In appendix 1, it is explicitly shown that for N-π, N-N scattering, the critical α for all points on the surface of singularities for the simplest 4-pt diagram lies entirely outside the interval (01) of the real axis, except those α corresponding to points on the curve of singularities as required by the Mandelstamm's theory. In appendix 2, a heuristic proof of the single dispersive relation independent of the momentum trausfer is provided. The proof rests on averaging over the azimuthal augle of meson momentum while the unclear momentum is oriented along the polar axis (here Breit system is emple-yed). In appendix 3, it is shown that hermiticity of certain variables leads to unitarity condition and thus one may hope to formulate the unitarity condition without encoanlering quadratic terms in the scattering amplitudes.
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