  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.
