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The Hirota transformation for the soliton solutions of the classicalSine-Gordon equation is suggestive of an extremely simple way for theconstruction of a nonlinear quantum-dynamical system of spin 1/2 particles thatis equivalent to the classical system over the soliton sector. The solitonsolution of the classical equation is mapped onto an operator, U, a nonlinearfunctional of the particle-number operators, that solves the classicalequation. Multi-particle states in the Fock space are the eigenstates of U; theeigenvalues are the soliton solutions of the Sine-Gordon equation. The factthat solitons can have positive as well negative velocities is reflected by thecharacterization of particles in the Fock space by two quantum numbers: a wavenumber k, and a spin projection, {\sigma} (= +-1). Thanks to the simplicity ofthe construction, incorporation of particle interactions, which induce solitoneffects that do not have a classical analog, is simple.

A nonlinear quantum dynamical system of spin 1/2 particles based on the classical Sine-Gordon Equation