Abstract
This paper is a discussion of the placement of integrable field theory models on a lattice of arbitrary spacing and the construction of the corresponding quantum integrals of motion. Two methods for producing local lattice models of both fundamental and nonfundamental types are covered. It is shown how projectors can be used to construct quasilocal lattice integrable models from quantum integrable field theories. The advantage of the projector method over other methods is the preservation of the original [Formula: see text]-matrix. The integrable structure of the model is then left unchanged and the continuum integrals of motion are regained in the infinitesimal lattice limit.
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