A Quantization of Box-Ball Systems

Details A Quantization of Box-Ball Systems A Quantization of Box-Ball Systems

2004-04-27

arxiv.org/abs/nlin/0404047v1

Reviews. Math. Phys. 16 (2004) 1227-1258.

Nonlinear Sciences

Exactly Solvable and Integrable Systems

29 pages, 8 figures

Scientific paper

10.1142/S0129055X04002254

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.

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