Polarization geometry of magnetohydrodynamic turbulence

We introduce a geometric framework that organizes the second-order statistics of the Elasser fields into polarization states on generalized Poincar\'e spheres. In this representation, energy, cross-helicity, residual energy, and the phase lag between counter-propagating wave packets emerge as complementary polarization parameters. We derive a Bloch-analogue equation governing the evolution of polarization states and show that distinct polarization geometries are associated with different cascade dynamics. The framework predicts that transitions in the turbulent spectral scaling coincide with changes in the polarization state of the interacting modes.