EXACTNESS IN THE WENTZEL-KRAMERS-BRILLOUIN APPROXIMATION FOR SOME HOMOGENEOUS SPACES

Analysis of the Wentzel-Kramers-Brillouin (WKB) exactness in some homo geneous spaces is attempted. CPN as well as its noncompact counterpart D-N1 is studied. U(N+1) or U(N,1) based on the Schwinger bosons leads us to CPN or D-N,D-1 path integral expression for the quantity tr e(- iHT), with the aid of coherent states. The WKB approximation terminate s in the leading order and yields the exact result provided that the H amiltonian is given by a bilinear form of the creation and the annihil ation operators. An argument on the WKB exactness to more general case s is also made. (C) 1995 American Institute of Physics.