Semiclassical treatment of spin system by means of coherent states

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Abstract
The semiclassical time-dependent propagator is studied in terms of the SU(2) coherent states for spin systems. The first- and second-order terms are obtained by means of a detailed calculation. While the first-order term was established in the earlier days of coherent states the second-order one is a subject of contradiction. The present approach is developed through a polygonal expansion of the discontinuous paths that enter the path integral. The results here presented are in agreement with only one of the previous approaches, i.e., the one developed on Glauber’s coherent states by means of a direct WKB approximation. It is shown that the present approach gives the exact result in a simple case where it is also possible to observe differences with previous works.