无限平面弦：尖点、辫和孤子激发
Infinite planar string: cusps, braids and soliton exitations
摘要：
我们研究了$(2+1)D$时空中的无限弦，它可以看作是空间平面上直线的激发。我们还提出了这些对象的哈密顿描述，不同于标准的哈密顿描述的字符串。哈密顿变量分为两个独立的组：“内部”和“外部”变量。第一个在时空变换下是不变的，并且与世界片的第二种形式有关。“外部”变量定义了世界片嵌入时空的过程。构造的相空间是非平凡的，因为有限数量的约束纠缠这些群体的变量。第一组变量构成了一阶谱问题对的系数;这些问题的解对于弦世界表的重建是必要的。我们考虑了对应于谱问题的“N-孤子”解的激发，并证明了重构弦具有尖点。这些点的世界线形成各种拓扑的辫子。
英文摘要：
We investigate infinite strings in $(2+1)D$ space-time, which may be considered as excitations of straight lines on the spatial plane. We also propose the hamiltonian description of such objects that differs from the standard hamiltonian description of the string. The hamiltonian variables are separated into two independent groups: the "internal" and "external" variables. The first ones are invariant under space-time transformations and are connected with the second form of the world-sheet. The "external" variables define the embedding of the world-sheet into space-time. The constructed phase space is nontrivial because the finite number of constraints entangles the variables from these groups. First group of the variables constitute the coefficients for the pair of first-order spectral problems; the solution of these problems is necessary for the reconstruction of the string world-sheet. We consider the excitations, which correspond to "N- soliton" solution of the spectral problem, and demonstrate that the reconstructed string has cuspidal points. World lines of such points form braids of various topologies.
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