从霍普夫纤维化到奇异的因果替换
From Hopf fibrations to exotic causal replacements
摘要：
拓扑孤子在物理学的几个领域都是相关的[1]。最近，这些配置已经在流体力学[2]，玻色-爱因斯坦凝聚体[3]，铁磁性[4]，打结光[5]和非阿贝尔规范理论[6]等不同的背景下进行了研究。在本文中，我们解决的问题，波传播的静态霍普夫孤子的背景下，妮可模型。工作在几何光学的限制，我们表明，一些非平凡的透镜效应出现由于非线性相互作用，只要理论保持双曲。我们的结论是，类似的效果是很可能发生在有效场论的特点是一个拓扑不变，如Skyrme模型的π介子。
英文摘要：
Topological solitons are relevant in several areas of physics [1]. Recently, these configurations have been investigated in contexts as diverse as hydrodynamics [2], Bose-Einstein condensates [3], ferromagnetism [4], knotted light [5] and non-abelian gauge theories [6]. In this paper we address the issue of wave propagation about a static Hopf soliton in the context of the Nicole model. Working within the geometrical optics limit we show that several nontrivial lensing effects emerge due to nonlinear interactions as long as the theory remains hyperbolic. We conclude that similar effects are very likely to occur in effective field theories characterized by a topological invariant such as the Skyrme model of pions.
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