Regular and Chaotic Dynamics

, Volume 14, Issue 2, pp 218–222 | Cite as

Towards the proof of complete integrability of quantum elliptic many-body systems with spin degrees of freedom

  • J. DittrichEmail author
  • V. I. Inozemtsev
Research Articles


We consider the problem of finding integrals of motion for quantum elliptic Calogero-Moser systems with arbitrary number of particles extended by introducing spinexchange interaction. By direct calculation, after making certain ansatz, we found first two integrals — quite probably, lowest nontrivial members of the whole commutative ring. This result might be considered as the first step in constructing this ring of the operators which commute with the Hamiltonian of the model.

Key words

quantum elliptic spin systems transpositions integrability 

MSC2000 numbers

33E05 05E10 37K60 


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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Nuclear Physics Institute ASCRŘežCzech Republic
  2. 2.Laboratory of Theoretical PhysicsJINRDubna, Moscow RegionRussia

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