Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-09-06
J.Math.Phys. 37 (1996) 567-602
Physics
High Energy Physics
High Energy Physics - Theory
43 pages, LaTeX, minor change to correct a misprint
Scientific paper
10.1063/1.531430
\(\Un{N}\) coherent states over Grassmann manifold, \(\grsmn{N}{n}\simeq\Un{N}/ (\Un{n}\times \Un{N-n})\), are formulated to be able to argue the WKB-exactness, so called the localization of Duistermaat-Heckman, in the path integral representation of a character formula. The exponent in the path integral formula is proportional to an integer \(k\) that labels the \(\Un{N}\) representation. Thus when \(k \rightarrow\infty\) a usual semiclassical approximation, by regarding \(k \sim 1 / \hbar\), can be performed yielding to a desired conclusion. The mechanism of the localization is uncovered by means of a view from an extended space realized by the Schwinger boson technique.
Fujii Kazuyuki
Kashiwa Taro
Sakoda Seiji
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