Coherent states, Path integral, and Semiclassical approximation

Details Coherent states, Path integral, and Semiclassical approximation Coherent states, Path integral, and Semiclassical approximation

1994-09-20

arxiv.org/abs/hep-th/9409116v2

J.Math.Phys.36:3232-3253,1995

Physics

High Energy Physics

High Energy Physics - Theory

latex 33 pages and 2 figures(uuencoded postscript file), KYUSHU-HET-19 We have corrected the proof of the WKB-exactness in the

Scientific paper

10.1063/1.531028

Using the generalized coherent states we argue that the path integral formulae for $SU(2)$ and $SU(1,1)$ (in the discrete series) are WKB exact,if the starting point is expressed as the trace of $e^{-iT\hat H}$ with $\hat H$ being given by a linear combination of generators. In our case,WKB approximation is achieved by taking a large ``spin'' limit: $J,K\rightarrow \infty$. The result is obtained directly by knowing that the each coefficient vanishes under the $J^{-1}$($K^{-1}$) expansion and is examined by another method to be legitimated. We also point out that the discretized form of path integral is indispensable, in other words, the continuum path integral expression leads us to a wrong result. Therefore a 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.

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