标题： 规范等价性和跨维度扰动：点涡旋 显示英文标题

标题： Gauge equivalence and transdimensional perturbation: point vortices

摘要： 存在平面四点涡旋的泊松约化的一个显式解，其中三个涡旋强度相等且总涡度为零。 这个解是一个哈密顿系统，在具有对称性破缺参数的统一辛相空间上，通过附加冗余状态获得。 尽管单个点涡旋没有质量属性，但存在一些圆形集合，其集体动力学类似于自由有质量粒子，展示了从规范对称性破缺中出现有限维动力学的情况。 这些集合的内部振动与其集体运动耦合，并且具有与德布罗意波长相同的函数形式。 显示英文摘要

摘要： There is an explicit resolution of the Poisson reduction of four planar point vortices, in the case that three of the vortex strengths are equal and the total vorticity is zero. The resolution, a Hamiltonian system on a unified symplectic phase space with a symmetry breaking parameter, is obtained by appending redundant states. Though single point vortices do not have the attribute of mass, there are circular assemblages with the collective dynamics of free massive particles, demonstrating a finite dimensional dynamics where mass emerges from a gauge symmetry breaking. The internal vibration of these assemblages is coupled to their collective motion and has the same functional form as the de Broglie wavelength.