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 matrix-valued non-Abelian Berry holonomies acting on degenerate internal states associated with symmetry groups G. These holonomies arise from internal degeneracyand topological linking rather than from braid-group statistics. We show how effective gauge interactions emerge from constrained collective dynamics and presentan analogue mapping between vortex network structures and Standard Model–like internal quantum numbers.
Alex Smith (Mon,) studied this question.