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