Nonlinear bosonization and the anomalous Hall effect

We study various aspects of anomalous Hall effect using nonlinear bosonization. Nonlinear bosonization offers both perturbative and non-perturbative techniques to study Fermi and non-Fermi liquids. This approach naturally leads to a multidimensional bosonized description with nonlinear corrections fixed by the geometry of the Fermi surface. We find how Berry curvature can be captured in the nonlinear bosonization framework, establishing the connections with the anomalous Hall effect.