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Coherent states over Grassmann manifolds and the WKB-exactness in path integral

Kazuyuki Fujii·Taro Kashiwa·Seiji Sakoda
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Abstract

\(\Un{N}\) 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.

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Kazuyuki Fujii, Taro Kashiwa, Seiji Sakoda. 1995-09-21. Coherent states over Grassmann manifolds and the WKB-exactness in path integral. https://doi.org/10.1063/1.531430

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