We present the saddle-point approximation for the effective Hamiltonian of the quantum kink in two-dimensional linear sigma models to all orders in the time-derivative expansion. We show how the effective Hamiltonian can be used to obtain semiclassical soliton form factors, valid at momentum transfers of order the soliton mass. Explicit results, however, hinge on finding an explicit solution to a new wave-like partial differential equation, with a time-dependent velocity and a forcing term that depend on the solution. In the limit of small momentum transfer, the effective Hamiltonian reduces to the expected form, namely H = sqrt{P^2 + M^2}, where M is the one-loop corrected soliton mass, and soliton form factors are given in terms of Fourier transforms of the corresponding classical profiles.

中文翻译：

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加速孤子

我们在时间导数展开式中，针对所有阶次的二维线性sigma模型，给出了量子纽结的有效哈密顿量的鞍点近似。我们展示了如何使用有效的哈密顿量获得半经典的孤子形状因子，在阶次孤子质量的动量传递中有效。但是，明确的结果取决于找到一个新的波状偏微分方程的显式解，其时变速度和强迫项取决于解。在小动量传递的极限中，有效的哈密顿量减少为预期形式，即H = sqrt {P ^ 2 + M ^ 2}，其中M是单环校正孤子质量，并且孤子形状因数表示为相应的经典轮廓的傅立叶变换。