OPERATOR ALGEBRA FOR STOCHASTIC DYNAMICS AND THE HEISENBERG CHAIN

The operator algebra C(S - D) = CD - DC = (S + D)C, DD + DD = DS - SD is shown to represent the stochastic dynamics of symmetric hopping of hard-core particles in one dimension and to describe the Heisenberg qu antum chain. The particle or spin state is specified by strings of the operators C and D, and S is related to a current. Recursive reduction s and matrix representations are used to obtain stationary and time-de pendent properties, including the evolving profile for a system driven by a density gradient between open boundaries. Generalizations to oth er models are outlined.