A Quantization of Box-Ball Systems
Rei Inoue, Atsuo Kuniba, Masato Okado
Abstract
An L operator is presented related to an infinite dimensional limit of the fusion R matrices for Uq(A(1)n-1) and Uq(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.
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