A Quantization of Box-Ball Systems
arXiv:nlin/0404047 · doi:10.1142/S0129055X04002254
Abstract
An L operator is presented related to an infinite dimensional limit of the fusion R matrices for U_q(A^{(1)}_{n-1}) and U_q(D^{(1)}_n). It is factorized into the local propagation operators which quantize the deterministic dynamics of particles and antiparticles in the soliton cellular automata known as the box-ball systems and their generalizations. Some properties of the dynamical amplitudes are also investigated.
29 pages, 8 figures