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Journal of Mathematical Physics : The O(1)-Kepler problems

By Guowu Meng

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Book Id: WPLBN0002169541
Format Type: PDF eBook :
File Size: Serial Publication
Reproduction Date: 21 October 2008

Title: Journal of Mathematical Physics : The O(1)-Kepler problems  
Author: Guowu Meng
Volume: Issue : October 2008
Language: English
Subject: Science, Physics, Natural Science
Collections: Periodicals: Journal and Magazine Collection, Journal of Mathematical Physics Collection
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Publication Date:
Publisher: American Institute of Physics

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Meng, G. (n.d.). Journal of Mathematical Physics : The O(1)-Kepler problems. Retrieved from http://worldlibrary.in/


Description
Description: Let n ≥ 2 be an integer. To each irreducible representation σ of O(1), an O(1)-Kepler problem in dimension n is constructed and analyzed. This system is super integrable and when n = 2 it is equivalent to a generalized MICZ (McIntosh-Cisneros-Zwanziger)-Kepler problem in dimension 2. The dynamical symmetry group of this system is (2n,) with the Hilbert space of bound states H(σ) being the unitary highest weight representation of (2n,) with highest weight which occurs at the rightmost nontrivial reduction point in the Enright–Howe–Wallach classification diagram for the unitary highest weight modules. (Here |σ| = 0 or 1 depending on whether σ is trivial or not.) Furthermore, it is shown that the correspondence σ↔H(σ) is the theta correspondence for dual pair (O(1),Sp(2n,))⊆Sp(2n,).

 

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