Fermi-Liquid Description of a Single-Component Fermi Gas with $p$-Wave Interactions

We study the Fermi liquid properties of a single component Fermi gas with $p$-wave interactions. In the weak repulsive limit, we obtain exact perturbative expansions for the ground state energy, the chemical potential, and the effective mass of the Landau quasiparticle up to second order in scattering volume $a$. We also calculated the corresponding Landau functions and Landau parameters and show that they satisfy the general Fermi liquid identities. Using the Landau transport equation, we show that undamped zero sound only appears in the second order in scattering volume, in contrast to the $s$-wave case.