Homological classification of topological terms in sigma models on homogeneous spaces
Homological classification of topological terms in sigma models on homogeneous spaces
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齐次空间上 sigma 模型中拓扑项的同调分类
DOI：
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发表时间：
2018
影响因子：
5.4
通讯作者：
B. Gripaios
中科院分区：
文献类型：
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作者：
Joe Davighi;B. Gripaios
我们对可能出现在基于从任意世界体积流形到齐次空间G/H（其中G是任意李群，H <$G）的映射的非线性sigma模型中的拓扑项进行分类（在某种意义上是精确的）。我们导出了拓扑项G-不变性的一个新条件，这是必要和充分的（至少当G是连通的），并讨论了量子力学和量子场论中的各种例子。在目前的工作中，我们讨论的条款，可以写在G/H（可能只有本地定义）的微分形式，导致一个行动，显然是本地的。这些项有两种类型，典型的量子力学例子是阿哈罗诺夫-玻姆效应和狄拉克粒子。这种分类是基于这样的观察，即对于拓扑项，从世界体积到G/H的映射可以被G/H上的奇异同调圈所取代。在即将发表的论文中，我们将结果应用于希格斯玻色子是复合物的唯象模型。
A bstractWe classify the topological terms (in a sense to be made precise) that may appear in a non-linear sigma model based on maps from an arbitrary worldvolume manifold to a homogeneous space G/H (where G is an arbitrary Lie group and H ⊂ G). We derive a new condition for G-invariance of topological terms, which is necessary and sufficient (at least when G is connected), and discuss a variety of examples in quantum mechanics and quantum field theory. In the present work we discuss only terms that may be written in terms of (possibly only locally-defined) differential forms on G/H, leading to an action that is manifestly local. Such terms come in one of two types, with prototypical quantum-mechanical examples given by the Aharonov-Bohm effect and the Dirac monopole. The classification is based on the observation that, for topological terms, the maps from the worldvolume to G/H may be replaced by singular homology cycles on G/H. In a forthcoming paper we apply the results to phenomenological models in which the Higgs boson is composite.
影响因子：
8.6
作者：
B. Gripaios;Dave Sutherland
通讯作者：
B. Gripaios;Dave Sutherland