Seminar 01.04.2026: Anton Sutulin (BLTP, JINR, Dubna)
Title: Integrability of supersymmetric Calogero Moser models Abstract: We analyze the integrability of the N-extended supersymmetric Calogero-Moser model. We explicitly construct the Lax pair for this system, which properly reproduces all equations of motion. After adding a supersymmetric oscillator potential we reduce the latter to solving dU/dt = AU 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 5-th power in the momenta, for the N=2 supersymmetric model. The additional, non-involutive, conserved charges needed for a maximal superintegrability of this model are also found.
Title: Integrability of supersymmetric Calogero Moser models Abstract: We analyze the integrability of the N-extended supersymmetric Calogero-Moser model. We explicitly construct the Lax pair for this system, which properly reproduces all equations of motion. After adding a supersymmetric oscillator potential we reduce the latter to solving dU/dt = AU 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 5-th power in the momenta, for the N=2 supersymmetric model. The additional, non-involutive, conserved charges needed for a maximal superintegrability of this model are also found.