Universality Classes Of Fermionic Vacua

This chapter discusses effective theories of quantum fermionic liquids. In the low-energy limit, the type of the effective theory depends on the structure of the quasiparticle spectrum, which in turn is determined by topology in momentum space (p-space topology). The p-space topology distinguishes three main generic classes of the stable fermionic spectrum in the quantum vacuum of a 3+1 fermionic system: vacua with Fermi surfaces, vacua with Fermi points, and vacua with a fully gapped fermionic spectrum. Fermi surface is stable because it represents the topological object — the vortex in...

This chapter discusses effective theories of quantum fermionic liquids. In the low-energy limit, the type of the effective theory depends on the structure of the quasiparticle spectrum, which in turn is determined by topology in momentum space (p-space topology). The p-space topology distinguishes three main generic classes of the stable fermionic spectrum in the quantum vacuum of a 3+1 fermionic system: vacua with Fermi surfaces, vacua with Fermi points, and vacua with a fully gapped fermionic spectrum. Fermi surface is stable because it represents the topological object — the vortex in momentum space. As a result, Fermi liquids with Fermi surface share the properties of their simplest representative: weakly interacting Fermi gas. The low-energy physics of the interacting particles in a Fermi liquid is equivalent to the physics of a gas of quasiparticles moving in collective Bose fields produced by all other particles. Another topological object in p-space is the hedgehog, which is responsible for stability of Fermi points. Example of vacuum of the Fermi-point universality class is provided by ³He-A. Near the Fermi point the effective relativistic field theory emerges with emerging Weyl fermions, gauge fields, and gravity. The chapter discusses p-space and r-space topology, topological invariant for Fermi surface and Fermi points in terms of Green's function, Landau and non-Landau Fermi liquids, collective modes of the Fermi surface, volume of the Fermi surface as invariant of adiabatic deformations, collective modes of vacuum with Fermi points (electromagnetic and gravitational fields), and manifolds of zeros in p-space of higher dimensions.