Speaker
Description
In the fractional quantum Hall effect, the topological quenching of kinetic energy elevates spatial geometry to the primary dynamical degree of freedom. We demonstrate that macroscopic charge dynamics can be rigorously formulated as a reduced classical phase space of two-dimensional unimodular vielbeins and the physical charge density is exactly identified with the scalar curvature of the vielbein's torsionless spin connection. Consequently, the Girvin-MacDonald-Platzman (GMP) algebra emerges kinematically as the equivariant moment-map algebra of area-preserving diffeomorphisms.
Extending this geometry to spinful fluids, we construct a commutative, Wess-Zumino-like action coupling two vielbein sheets to a local spin frame. This provides a direct physical intuition akin to frame-dragging: because the underlying spatial coordinates are intrinsically noncommutative, applying spatially varying spin rotations inevitably drags the orbital fluid labels. The spin-GMP algebra is shown to be hardwired into this geometry — emerging as frame-dragging on a spin-entangled spatial background.