U（1）Higgs玻色子的整体演化：非线性稳定性和一致能量界
Global evolution of the U(1) Higgs Boson: nonlinear stability and uniform energy bounds
摘要：
利用双曲叶理方法，建立了$U(1)$标准模型基态的非线性稳定性。这相当于为将（狄拉克、标量、规范）大质量方程耦合在一起的非线性波-克莱因-戈登系统的初值问题建立了一个全局时间理论。特别是，我们在这里调查的狄拉克方程，并考虑一个新的能量泛函定义的双曲面叶状闵可夫斯基时空这个领域。我们提供了一个新的狄拉克方程的衰减结果是均匀的质量系数，从而允许狄拉克质量系数是任意小的。此外，我们得到的希格斯场和规范玻色子是统一的双曲时间变量的能量界限。
英文摘要：
Relying on the hyperboloidal foliation method, we establish the nonlinear stability of the ground state of the $U(1)$ standard model of electroweak interactions. This amounts to establishing a global-in-time theory for the initial value problem for a nonlinear wave-Klein-Gordon system that couples (Dirac, scalar, gauge) massive equations together. In particular, we investigate here the Dirac equation and consider a new energy functional for this field defined with respect to the hyperboloidal foliation of Minkowski spacetime. We provide a novel decay result for the Dirac equation which is uniform in the mass coefficient, and thus allows for the Dirac mass coefficient to be arbitrarily small. Furthermore we obtain energy bounds for the Higgs fields and gauge bosons that are uniform with respect to the hyperboloidal time variable.
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