EXACTNESS IN THE WKB APPROXIMATION FOR SOME HOMOGENEOUS SPACES

Abstract

Analysis of the WKB exactness in some homogeneous spaces is attempted. $C{P}^N$ as well as its noncompact counterpart $D_{N,1}$ is studied. $U(N+1)$ or U(N,1) based on the Schwinger bosons leads us to $C{P}^N$ or $D_{N,1}$ path integral expression for the quantity, $\mathrm{tr}{e}^{-iHT}$, with the aid of coherent states. The WKB approximation terminates in the leading order and yields the exact result provided that the Hamiltonian is given by a bilinear form of the creation and the annihilation operators. An argument on the WKB exactness to more general cases is also made.

27pages, latex, no figures

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• Coherent states, Path integral, and Semiclassical approximation
• Symplectic Manifolds, Coherent States and Semiclassical Approximation
• Coherent State Quantization of SU(N) Non-Abelian Chern-Simons Particles

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