  We present a formulation of magnetohydrodynamics which can be used to
describe the evolution of strong magnetic fields in neutron star interiors. Our
approach is based on viewing magnetohydrodynamics as a theory with a one-form
global symmetry and developing an effective field theory for the hydrodynamic
modes associated with this symmetry. In the regime where the local velocity and
temperature variations can be neglected, we derive the most general
constitutive relation consistent with symmetry constraints for the electric
field in the presence of a strong magnetic field. This constitutive relation
not only reproduces the phenomena of Ohmic decay, ambipolar diffusion, and Hall
drift derived in a phenomenological model by Goldreich and Reisenegger, but
also reveals new terms in the evolution of the magnetic field which cannot
easily be seen from such microscopic models. This formulation gives predictions
for novel diffusion behaviors of small perturbations around a constant
background magnetic field, and for the two-point correlation functions among
various components of the electric and magnetic fields.
