Several path integral representations for the $T$-matrix in nonrelativisticpotential scattering are given which produce the complete Born series whenexpanded to all orders and the eikonal approximation if the quantumfluctuations are suppressed. They are obtained with the help of "phantom"degrees of freedom which take away explicit phases that diverge for asymptotictimes. Energy conservation is enforced by imposing a Faddeev-Popov-likeconstraint in the velocity path integral. An attempt is made to evaluatestochastically the real-time path integral for potential scattering andgeneralizations to relativistic scattering are discussed.
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机译:给出了非相对论势散射中$ T $-矩阵的几种路径积分表示,当扩展到所有阶数时,它们会产生完整的Born级数;如果抑制了量子涨落,则将产生理想的近似值。它们是在“幻像”自由度的帮助下获得的,它消除了渐近时间发散的明确阶段。通过在速度路径积分中施加类似于Faddeev-Popov的约束来强制节能。尝试随机地评估潜在散射的实时路径积分,并讨论了广义相对论散射。
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