Journal of Applied Mathematics 
Volume 1 (2001), Issue 2, Pages 47-68
doi:10.1155/S1110757X01000055

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

Abstract

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.