论文标题
$ \ mathbb {r}^{n，1} $和杀死矢量代数的规范形式的同构性一个字符串的完整可集成性
Complete Integrability of Cohomogeneity-one strings in $\mathbb{R}^{n,1}$ and Canonical Form of Killing Vector Algebra
论文作者
论文摘要
已经研究了flat Space $ \ mathbb {r}^{n，1} $的连续性运动方程。我们首先将杀死向量字段的可能形式分类为$ \ mathbb {r}^{n，1} $，在Poincaré集团的适当操作之后。然后，确定了用于同一性的Hamiltonian的所有可能形式 - 一个Nambu-Goto弦。已经表明，该系统始终具有最大独立的，配对通勤的保守量，即完全可以集成。我们还确定了二维非公共谎言代数的杀戮载体基础的所有可能的坐标形式。
The equation of motion for comohogeneity-one Nambu-Goto strings in flat space $\mathbb{R}^{n,1}$ has been investigated. We first classify possible forms of the Killing vector fields in $\mathbb{R}^{n,1}$ after appropriate action of the Poincaré 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 2-dimensional non-commutative Lie algebra.
