Fermi Liquid Theory
Landau's Fermi liquid theory is one of the most successful frameworks in condensed matter physics. Starting from the free Fermi gas, it explains how electron-electron interactions can be incorporated through the concept of quasiparticles — excitations that behave like dressed electrons with renormalized mass and lifetime.
The key insight is adiabatic continuity: if interactions are turned on slowly, the ground state of the interacting system evolves smoothly from the non-interacting Fermi sea. The low-energy excitations maintain a one-to-one correspondence with those of the free gas, but acquire an effective mass $m^*$ and interact via Landau parameters $F_l^{s,a}$.
Chapters
1. Free Fermi Gas
Fermi-Dirac statistics, density of states, Sommerfeld expansion, specific heat, and Pauli paramagnetism.
2. Quasiparticles
Adiabatic continuity, quasiparticle concept, spectral function, self-energy, and lifetime near the Fermi surface.
3. Landau Fermi Liquid Theory
Energy functional, quasiparticle interaction, Landau parameters, effective mass, and compressibility.
4. Landau Parameters
Symmetric and antisymmetric Landau parameters, Pomeranchuk stability conditions, and measurable quantities.
5. Zero Sound & Collective Modes
Boltzmann transport for quasiparticles, zero sound vs first sound, and the collective mode spectrum.