狄拉克结构和模型上的汉密尔顿李代数

IF 0.7 4区 数学 Q3 MATHEMATICS
Noriaki Ikeda
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引用次数: 0

摘要

作为前辛流形和泊松流形上的哈密顿李代数体的推广,我们提出了一个哈密顿李代数体和狄拉克结构上的动量截面。一个哈密顿李代数体和一个动量截面推广了一个哈密顿g空间和一个辛流形上的动量映射。我们证明了这个新哈密顿李代数的一些性质,并以此为应用构造了一个力学。这些新的力学被称为量规泊松模型和量规狄拉克模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Hamilton Lie algebroids over Dirac structures and sigma models
We propose a Hamiltonian Lie algebroid and a momentum section over a Dirac structure as a generalization of a Hamiltonian Lie algebroid over a pre-symplectic manifold and one over a Poisson manifold. A Hamiltonian Lie algebroid and a momentum section generalize a Hamiltonian G-space and a momentum map over a symplectic manifold. We prove some properties of this new Hamiltonian Lie algebroid and construct a mechanics based on this structure as an application. These new mechanics are called the gauged Poisson sigma model and the gauged Dirac sigma model.
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来源期刊
CiteScore
1.00
自引率
20.00%
发文量
81
审稿时长
6-12 weeks
期刊介绍: Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.
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