Bosonization — 1D Luttinger Liquid

In 1D, fermionic quasiparticles are unstable: bosonization maps interacting fermions to free bosons (plasmons). The resulting Luttinger liquid has no Fermi surface but a Luttinger parameter K: K<1 (repulsive), K>1 (attractive). Spectral functions show power-law behavior: A(k,ω)~|ω|^α. The key signature is spin-charge separation — spin and charge excitations travel at different velocities v_s and v_c. Correlations decay as power laws set by K.