We construct a modified non-Bogomol’nyi-Prasad-Sommerfield sine-Gordon theory which supports stable static kinks of arbitrary topological degree $N$. We use this toy model to study problems that are interesting for higher-dimensional soliton theories supporting multisolitons. We construct a 2-kink collective coordinate model and use it to generate scattering trajectories, which are compared to full-field dynamics. We find that the approximation works well, but starts to fail as radiation becomes more important, due to our model becoming less Bogomol’nyi-Prasad-Sommerfield or when the initial kink velocities are large. We also construct the quantum 2-kink using various approximations and consider how these quantum corrections affect the binding energy of the 2-kink.

中文翻译：

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具有静态多扭结的修正正弦戈登理论


我们构建了一个修正的非 Bogomol'nyi-Prasad-Sommerfield sine-Gordon 理论，该理论支持任意拓扑度的稳定静态扭结 $N$ 。我们使用这个玩具模型来研究支持多孤子的高维孤子理论感兴趣的问题。我们构建了一个 2 扭结集体坐标模型，并用它来生成散射轨迹，并将其与全场动力学进行比较。我们发现该近似效果很好，但随着辐射变得更加重要，由于我们的模型变得越来越少 Bogomol'nyi-Prasad-Sommerfield 或当初始扭结速度很大时，该近似法开始失败。我们还使用各种近似来构造量子 2 扭结，并考虑这些量子校正如何影响 2 扭结的结合能。