The key point of the Hamiltonian formalism of Toda molecules is the commutativity of the Hamiltonians (tr yk, tr yl)=0, where y in GL(n) and (,) is a Poisson bracket associated with the classical r-matrix. To quantize the Toda molecule, we have to consider the q-analogue of the above formula. In this paper, we show the commutativity of the quantized first- and higher-order Hamiltonians (trq Xm, trq X)=0, where X is a matrix of quantum group GLq(n).
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)