Mathematical Sciences: Yang-Mills-Higgs Theory on R3 with Positive Coupling Constant

在这个项目中，主要研究者将研究 三维空间中的SU（2）Yang-Mills-Higgs方程 正耦合常数 她的目标是展示 SU（2）Yang-Mills的非极小有限作用临界点 任意正耦合三维空间中的Higgs泛函 常数，从而扩展了Taubes的工作为零的情况下， 耦合常数 陶贝斯能够建立一种 Liusternik-Schnirelman最小-最大理论适用于 在规范理论中出现的三维空间中的变分问题。 首席研究员希望建立类似的结果， 适用于正耦合常数的情况。 她将与Taubes和其他专家合作， 她的研究。 规范理论现在是一个基本领域， 数学物理它包含了许多深刻而重要的 数学家和物理学家感兴趣的问题。 其中一个问题涉及有限作用量的性质 解的某些变分方程，出现在杨- 三维空间中的米尔斯理论 首席研究员将专注于 在这个领域的一个重要问题，即显示存在 Yang-Mills的非极小有限作用临界点 在耦合常数为正时起作用。

In this project the principal investigator will study the SU(2) Yang-Mills-Higgs equations in three-space in the case of a positive coupling constant. Her goal is to show the existence of non-minimal finite-action critical points of the SU(2) Yang-Mills- Higgs functional in three-space with arbitrary positive coupling constant, thereby extending the work of Taubes for the case of zero coupling constant. Taubes was able to establish a form of the Liusternik-Schnirelman min-max theory that applies to the variational problems in three-space that arise in gauge theory. The principal investigator hopes to establish a similar result that applies in the case of positive coupling constant. She will collaborate with Taubes and other experts in the course of her research. Gauge theory is now one of the fundamental areas in mathematical physics. It contains a number of deep and important problems that are of interest to mathematicians and physicists. One of these problems involves the properties of finite-action solutions of certain variational equations that arise in the Yang- Mills theory in three-space. The principal investigator will focus on an important problem in this area, namely showing the existence of non-minimal finite-action critical points of the Yang-Mills functional in the case when the coupling constant is positive.