  In this paper, we construct the q-boson hopping model from the associated
quantum gauge theory. Inspired by the symmetries of quantum field theory, we
propose a new Bethe-ansatz to describe the wave functions of the q-boson
hopping model, and then we derive the q-boson algebras from this new ansatz.
Its study serves as a concrete case for a general program: the correspondence
between the bosonic integrable systems and the associated two-dimensional gauge
theories.
