We extend the emergent hydrodynamic framework for fermionic exchange established in Part I to multi-component vortex networks in a 3+1D quantized superfluid.Single framed vortex loops reproduce the Abelian π Berry phase corresponding to fermionic exchange. Multi-component and linked vortex networks exhibit matrixvalued non-Abelian Berry holonomies acting on degenerate internal states associated with symmetry groups G. These holonomies arise from internal degeneracy and topological linking rather than from braid-group statistics. We show how effective gauge interactions emerge from constrained collective dynamics and present a qualitative analogue mapping between vortex network structures and Standard Model–like internal quantum numbers.
Alex Smith (Tue,) studied this question.