Quantum spin formulation of the principal chiral model

We formulate the two-dimensional principal chiral model as a quantum spin m odel, replacing the classical fields by quantum operators acting in a Hilbe rt space, and introducing an additional, Euclidean time dimension. Using co herent state path integral techniques, we show that in the limit in which a large representation is chosen for the operators, the low energy excitatio ns of the model describe a principal chiral model in three dimensions. By d imensional reduction, the two-dimensional principal chiral model of classic al fields is recovered.