Bosonization of Non-Fermi Liquids*

Understanding non-Fermi liquids in dimensions higher than one remains one of the most formidable challenges in modern condensed matter physics. These systems, characterized by an abundance of gapless degrees of freedom and the absence of well-defined quasiparticles, defy conventional analytical frameworks. Inspired by recent work on the bosonization of Fermi surfaces [Delacretaz, Du, Mehta, and Son, Physical Review Research, 4, 033131 (2022)], we present a procedure for bosonizing non-Fermi liquids, which provides a holistic approach capable of addressing their intricate physics. Our method involves parameterizing the generalized fermionic distribution function through a bosonic field that describes frequency-dependent local variations of the chemical potential in momentum space. We propose an effective action that produces the collisionless quantum Boltzmann equation as its equation of motion and can straightforwardly be used for any dimension and Fermi surface of interest. Even at the quadratic order, this action reproduces highly non-trivial results obtainable only through involved analysis with alternative means. By offering a comprehensive description of the physics of non-Fermi liquids, our work stands as an important building block in advancing the comprehension of strange metals and associated phenomena.