计算环上可积分涡旋拓扑数的解析方法

arXiv - PHYS - Mathematical Physics Pub Date : 2024-03-27 DOI:arxiv-2403.18264

Kaoru Miyamoto, Atsushi Nakamula

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引用次数: 0

摘要

本文以 Chern-Simons-Higgs 理论的解析旋涡解为重点，构建了一种计算环上旋涡数的解析方法，而 Chern-Simons-Higgs 理论的指导方程是所谓的 Jackiw-Pi 方程。该方程是可积分涡方程之一，并被简化为柳维尔方程。希格斯场的连续性要求强烈限制了涡旋的特征和基本域。此外，还考虑了旋涡在环上的解压缩极限，其中偶尔会出现 "通量损失 "现象。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Analytic Approach for Computation of Topological Number of Integrable Vortex on Torus

An analytic method to calculate the vortex number on a torus is constructed, focusing on analytic vortex solutions to the Chern-Simons-Higgs theory, whose governing equation is the so-called Jackiw-Pi equation. The equation is one of the integrable vortex equations and is reduced to Liouville's equation. The requirement of continuity of the Higgs field strongly restricts the characteristics and the fundamental domain of the vortices. Also considered are the decompactification limits of the vortices on a torus, in which "flux loss" phenomena occasionally occur.

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arXiv - PHYS - Mathematical Physics

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