Validity of Boltzmann Kinetic Theory in Non-Fermi Liquids

Determine whether non-Fermi liquid metals admit a Boltzmann equation or equivalent kinetic description that remains valid for arbitrary ratios of frequency to temperature (ω/T) and at zero temperature, as is known to hold in Fermi liquid theory.

Background

The paper analyzes hydrodynamic and kinetic descriptions constrained by the LU(1) emergent symmetry and anomaly. While linearized hydrodynamics reproduces collisionless Fermi liquid behavior at leading order, the applicability of hydrodynamics at very low temperatures can be limited by long thermalization times, raising questions about descriptions valid at T=0.

In contrast, Fermi liquid theory supports a Boltzmann equation that holds at T=0 and for any ω/T. The author explicitly notes uncertainty about whether an analogous kinetic framework exists for non-Fermi liquids, highlighting a key unresolved issue for their dynamical description.