  We show that the stochastic dynamics of a large class of one-dimensional
interacting particle systems may be presented by integrable quantum spin
Hamiltonians. Using the Bethe ansatz and similarity transformations this yields
new exact results. In a complementary approach we generalize previous work and
present a new description of these and other processes and the related quantum
chains in terms of an operator algebra with quadratic relations. The full
solution of the master equation of the process is thus turned into the problem
of finding representations of this algebra. We find a two-dimensional
time-dependent representation of the algebra for the symmetric exclusion
process with open boundary conditions. We obtain new results on the dynamics of
this system and on the eigenvectors and eigenvalues of the corresponding
quantum spin chain, which is the isotropic Heisenberg ferromagnet with
non-diagonal boundary fields.
