Ascertain boost (K) invariance of the regularized Fermi-liquid-like description

Ascertain whether the regularized mean-field Fermi-liquid-like description derived from the effective Hamiltonian H_eff for electrons at half-filling of a Landau level truly exhibits boost (K) invariance once the quadratic mass term is eliminated, given that infrared singularities in the Hartree–Fock contribution lead to divergent higher-order coefficients and leave the invariance uncertain.

Background

To obtain a Fermi-liquid-like state compatible with dynamics projected to a Landau level, the authors regularize the effective Hamiltonian H_eff by adding terms that vanish on the physical space, aiming to eliminate the mass term and ensure boost invariance (K-invariance).

While the quadratic term can be removed, the Hartree–Fock procedure introduces infrared singularities that cause divergences in higher-order terms of the dispersion, leading the authors to question whether the resulting effective description truly satisfies boost invariance. Resolving this uncertainty is essential for a consistent low-energy FL-like theory in an isolated Landau level.