关于k-多余辛Marsden-Weinstein约化
On k-polycosymplectic Marsden-Weinstein reductions
AI总结：
本文改进k-多余辛约化理论，发展仿射李群作用去除等变性条件，提出k-多余弦辛约化理论，并应用于耦合振动弦与场对称哈密顿系统，同时给出k-余弦辛到l-余弦辛的时空约化。
摘要：
我们回顾并略微改进了已知的k-多余辛Marsden-Weinstein约化理论，通过发展k-多余辛动量映射的仿射李群作用理论，移除了对k-多余辛动量映射的一些技术性条件，从而消除了其余伴随等变性的必要性。然后，我们专注于分析k-多余辛流形的一个特殊情形，即所谓的纤维化流形，并研究它们的k-多余辛Marsden-Weinstein约化。先前的结果使我们能够设计出k-多余弦辛Marsden-Weinstein约化理论，这代表了我们的主要成果之一。我们的发现被应用于研究耦合振动弦，以及更一般地，具有场对称性的k-多余弦辛哈密顿系统。我们证明了k-多余弦辛几何可以被理解为k-多余辛几何的一个特定类型。最后，我们提出了一种从k-余弦辛到l-余弦辛的几何约化理论，该理论在k-余弦辛框架下几何地约化了时空变量。我们给出了这一结果对具有对称性的振动膜的一个应用。
英文摘要：
We review and slightly improve the known k-polysymplectic Marsden--Weinstein reduction theory by removing some technical conditions on k-polysymplectic momentum maps by developing a theory of affine Lie group actions for k-polysymplectic momentum maps, removing the necessity of their co-adjoint equivariance. Then, we focus on the analysis of a particular case of k-polysymplectic manifolds, the so-called fibred ones, and we study their k-polysymplectic Marsden--Weinstein reductions. Previous results allow us to devise a k-polycosymplectic Marsden--Weinstein reduction theory, which represents one of our main results. Our findings are applied to study coupled vibrating strings and, more generally, k-polycosymplectic Hamiltonian systems with field symmetries. We show that k-polycosymplectic geometry can be understood as a particular type of k-polysymplectic geometry. Finally, a k-cosymplectic to l-cosymplectic geometric reduction theory is presented, which reduces, geometrically, the space-time variables in a k-cosymplectic framework. An application of this latter result to a vibrating membrane with symmetries is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
