COHERENT STATES, PATH-INTEGRAL, AND SEMICLASSICAL APPROXIMATION

Using the generalized coherent states it is shown that the path integr al formulas for SU(2) and SU(1,1) (in the discrete series) are WKB exa ct, if it is started from the trace of e-iT((H) over cap), where (H) o ver 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 e xcept the leading term which indeed gives the exact result. It is furt her pointed out that the discretized form of path integral is indispen sable, in other words, the continuum path integral expression sometime s leads to a wrong result. Therefore great care must be taken when som e geometrical action would be adopted, even if it is so beautiful as t he starting ingredient of path integral. Discussions on generalized co herent states are also presented both from geometrical and simple osci llator (Schwinger boson) points of view. (C) 1995 American Institute o f Physics.