论文标题
扭结模量空间 - 集体坐标重新考虑
Kink Moduli Spaces -- Collective Coordinates Reconsidered
论文作者
论文摘要
Moduli空间 - 有限维，集体坐标流形 - 用于$ ϕ^4 $理论和正弦戈登理论中的扭结和反kink。 Lagrangian局限于模量空间的田间理论定义了降低的拉格朗日，将电势与动力学术语结合在一起，该术语可以解释为模量空间上的riemannian指标。模量的空间应进行指标完成，或在其边界上具有无限的电位。构建了针对扭结和扭结 - 安提克克键键配置的示例。尽管磁场仍然是真实的，但有时需要将扭结和反kink的幼稚位置坐标从真实值延伸到假想值。先前讨论的$ ϕ^4 $ kinks形状模式的零向量问题通过更好的坐标选择来解决。在正弦理论中，可以在临界能量分离散射和呼吸器（或摆动）溶液的临界能量的溶液中构建模量空间。在这里，能源保护与度量和潜力有关。这些模量空间上的减少动力学准确地重现了精确溶液在一系列能量上的性能。
Moduli spaces - finite-dimensional, collective coordinate manifolds - for kinks and antikinks in $ϕ^4$ theory and sine-Gordon theory are reconsidered. The field theory Lagrangian restricted to moduli space defines a reduced Lagrangian, combining a potential with a kinetic term that can be interpreted as a Riemannian metric on moduli space. Moduli spaces should be metrically complete, or have an infinite potential on their boundary. Examples are constructed for both kink-antikink and kink-antikink-kink configurations. The naive position coordinates of the kinks and antikinks sometimes need to be extended from real to imaginary values, although the field remains real. The previously discussed null-vector problem for the shape modes of $ϕ^4$ kinks is resolved by a better coordinate choice. In sine-Gordon theory, moduli spaces can be constructed using exact solutions at the critical energy separating scattering and breather (or wobble) solutions; here, energy conservation relates the metric and potential. The reduced dynamics on these moduli spaces accurately reproduces properties of the exact solutions over a range of energies.
