Journal of Applied Mathematics
Volume 1 (2001), Issue 2, Pages 47-68

Quantum relativistic Toda chain

G. Pronko1 and Sergei Sergeev2

1Institute for High Energy Physics, Protvino, Russia
2Joint Institute for Nuclear Research, Dubna, Russia

Received 19 September 2000; Revised 16 March 2001

Copyright © 2001 G. Pronko and Sergei Sergeev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Investigated is the quantum relativistic periodic Toda chain, to each site of which the ultra-local Weyl algebra is associated. Weyl’s q we are considering here is restricted to be inside the unit circle. Quantum Lax operators of the model are intertwined by six-vertex R-matrix. Both independent Baxter’s Q-operators are constructed explicitly as seria over local Weyl generators. The operator-valued Wronskian of R-matrix. Both independent Baxter’s Qs is also calculated.