ROTATIONS OF A CLOSED STRING WITH THE NAMBU LAGRANGIAN

In addition to widely known rotations of a linear string, rotations of a closed string, whose shape is more complex, also exist. For a close d string with the simplest Nambu geometric Lagrangian, solutions conta ining a singularity are investigated and the corresponding linear Regg e trajectories are determined. Two domains of solutions exist: (1) sol utions with the slope of trajectories larger than alpha'/4 and circula r velocities smaller than the velocity of light and (2) solutions with the slope of trajectories smaller than alpha'/4 and circular velociti es exceeding the velocity of light. A generalization of rotations of a string is considered, for which the right x = f(R)(tau - sigma) and t he left x = f(L)(tau + sigma) rotations are executed about axes differ ently oriented in space. These more complex solutions are not pure rot ations, but describe a continuous transition from the first to the sec ond domain of rotational solutions. These solutions can be quantized. The found states should be considered as a string model of quark-free hadrons, i.e., glueballs.