Complete integrability of cohomogeneity-one strings in Rn,1 and canonical form of Killing vector algebra

Abstract

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 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 two-dimensional noncommutative Lie algebra.