Monopoles, vortices and kinks in the framework of noncommutative geometry
Monopoles, vortices and kinks in the framework of noncommutative geometry
复制标题
非交换几何框架中的单极子、涡旋和扭结
DOI：
10.1103/physrevd.56.2291
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发表时间：
1997
影响因子：
5
通讯作者：
C. Ting
中科院分区：
文献类型：
--
作者：
Edward Teo;C. Ting
非对易微分几何允许标量场被视为规范连接，尽管是在离散空间上。我们解释了基本的规范原理如何对应于物理学对真空态选择的独立性，如果它是非唯一的。一个结果是杨-米尔斯-希格斯理论可以被重新表述为具有{bold Z}{sub 2}内部结构的欧氏空间上的广义杨-米尔斯规范理论。通过将Hodge星星运算推广到这个非对易空间，我们能够定义任意维规范曲率形式的自对偶性概念。事实证明，BPS单极，临界耦合涡，扭结都是在各自的维度自对偶解决方案。然后，我们证明，在这个统一的形式主义，静态孤立子解决方案杨米尔斯希格斯系统只存在于一个，两个和三个空间维度。{版权} {美国物理学会}
Noncommutative differential geometry allows a scalar field to be regarded as a gauge connection, albeit on a discrete space. We explain how the underlying gauge principle corresponds to the independence of physics on the choice of vacuum state, should it be nonunique. A consequence is that Yang-Mills-Higgs theory can be reformulated as a generalized Yang-Mills gauge theory on Euclidean space with a {bold Z}{sub 2} internal structure. By extending the Hodge star operation to this noncommutative space, we are able to define the notion of self-duality of the gauge curvature form in arbitrary dimensions. It turns out that BPS monopoles, critically coupled vortices, and kinks are all self-dual solutions in their respective dimensions. We then prove, within this unified formalism, that static soliton solutions to the Yang-Mills-Higgs system exist only in one, two, and three spatial dimensions. {copyright} {ital 1997} {ital The American Physical Society}