由GL(n, R)群流形上测地线运动导出的广义Calogero-Moser-Sutherland模型
摘要
表明赋予双不变度量 d s^2 = tr(g^{-1} d g)^2 的GL(n, R)群流形上的测地线运动对应于双曲n粒子Calogero-Moser-Sutherland模型的推广。特别地,考虑SO(n, R)群作用的主轨道层,我们得到遵从SO(n, R) \bigoplus SO(n, R)代数的两类内部自由度的广义n粒子Calogero-Moser-Sutherland系统动力学。对SO(n, R)群作用的奇异轨道层,测地线运动对应于某种意义上描述具有不同质量粒子的Calogero-Moser-Sutherland模型的某些形变。质量比依赖于奇异轨道层的类型并由其退化度决定。利用系统离散与连续对称性的约化,展示了与II A_n Euler-Calogero-Moser-Sutherland模型的关系。
引用
@article{arxiv.nlin/0103047,
title = {Generalized Calogero-Moser-Sutherland models from geodesic motion on GL(n, R) group manifold},
author = {A. M. Khvedelidze and D. M. Mladenov},
journal= {arXiv preprint arXiv:nlin/0103047},
year = {2009}
}
备注
16 pages, LaTeX, no figures. V2: Typos corrected, two references added. V3: Abstract changed, typos corrected, a few formulas and references added. The presentation in the last section has been clarified and it was restricted to the case of GL(3, R) group, the analysis of GL(4, R) will be given elsewhere. V4: Minor corrections in the whole text, more formulas and references added, accepted for publication in PLA