论文标题
超对称calogero-moser模型的一致性
Integrability of supersymmetric Calogero-Moser models
论文作者
论文摘要
我们分析了$ {\ cal n} $ - 扩展超对称Calogero-Moser模型的集成性。我们明确地为此系统明确构造了Lax Pair $ \ {l，A \} $，该系统正确地重现了所有运动方程。添加超对称振荡器电位后，我们将后者降低到求解$ \ dot {u} \，{=} \，a \，u $，time Evolution Evolution Operator $ u（t）$。但是，玻色粒变量在封闭轨迹上独立于$ u $而发展，这是促进性所必需的。为了可视化保守电流的结构，我们得出了liouville的完整集合，最高可达第五功率，对于$ {\ cal n} {=} {=} \，2 $ supersymmetrictric模型。还发现了该模型的最大可凝性所需的额外的，无接收的，保守的电荷。
We analyze the integrability of the ${\cal N}$-extended supersymmetric Calogero-Moser model. We explicitly construct the Lax pair $\{L,A\}$ for this system, which properly reproduces all equations of motion. After adding a supersymmetric oscillator potential we reduce the latter to solving $\dot{U}\,{=}\,A\,U$ for the time evolution operator $U(t)$. The bosonic variables, however, evolve independently of $U$ on closed trajectories, as is required for superintegrability. To visualize the structure of the conserved currents we derive the complete set of Liouville charges up to the fifth power in the momenta, for the ${\cal N}{=}\,2$ supersymmetric model. The additional, non-involutive, conserved charges needed for a maximal superintegrability of this model are also found.
