Abstract
U(N) coherent states over Grassmann manifold, GN,n≂U(N)/(U(n)×U(N−n)), are formulated to be able to argue the WKB exactness in the path integral representation of a character formula. The phenomena is the so-called localization of Duistermaat–Heckman. The exponent in the path integral formula is proportional to an integer k labeling the U(N) representation. Thus, when k→∞ a usual semiclassical approximation, by regarding k∼1/ℏ, can be performed to yield a desired conclusion. The mechanism of the localization is uncovered by the help of the (generalized) Schwinger boson technique. The discussion on the Feynman kernel is also presented.
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