COHERENT STATES, PATH-INTEGRAL, AND SEMICLASSICAL APPROXIMATION

Using the generalized coherent states it is shown that the path integral formulas for SU(2) and SU(1,1) (in the discrete series) are WKB exact, if it is started from the trace of e-iT((H) over cap), where (H) over cap is given by a linear combination of generators. In this case, the WKB approximation is achieved by taking a large ''spin'' limit: J,K-->infinity, under which it is found that each coefficient Vanishes except the leading term which indeed gives the exact result. It is further pointed out that the discretized form of path integral is indispensable, in other words, the continuum path integral expression sometimes leads to a wrong result. Therefore great care must be taken when some geometrical action would be adopted, even if it is so beautiful as the starting ingredient of path integral. Discussions on generalized coherent states are also presented both from geometrical and simple oscillator (Schwinger boson) points of view. (C) 1995 American Institute of Physics.