The equation of motion for cohomogeneity-one Nambu–Goto strings in flat space Rn,1 has been investigated. We first classify possible forms of the Killing vector fields in Rn,1 after appropriate action of the Poincare group. Then, all possible forms of the Hamiltonian for the cohomogeneity-one Nambu–Goto strings are determined. It has been shown that the system always has the maximum number of functionally independent, pair-wise commuting conserved quantities, i.e., it is completely integrable. We have also determined all the possible coordinate forms of the Killing vector basis for the two-dimensional noncommutative Lie algebra.

中文翻译：

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Rn,1 中同质一串的完全可积性和 Killing 向量代数的规范形式

已经研究了平坦空间 Rn,1 中同质一 Nambu-Goto 弦的运动方程。在 Poincare 组的适当动作之后，我们首先对 Rn,1 中的 Killing 向量场的可能形式进行分类。然后，确定了同质为一的 Nambu-Goto 弦的哈密顿量的所有可能形式。已经表明，系统总是具有最大数量的功能独立、成对交换守恒量，即它是完全可积的。我们还确定了二维非交换李代数的 Killing 向量基的所有可能坐标形式。