Bosonization of current-current interactions

Abstract

We discuss a generalization of the conventional bosonization procedure to the case of current-current interactions which get their natural representation in terms of current instead of fermion number density operators. A consistent bosonization procedure requires a geometrical quantization of the hamiltonian action of $W_{\infty }$ on its coadjoint orbits. An integrable example of a nontrivial realization of this symmetry is presented by the Calogero-Sutherland model. For an illustrative nonintegrable example we consider transverse gauge interactions and calculate the fermion Green function.

15 pages, TeX, C Version 3.0, Princeton preprint

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• Parquet solution for a flat Fermi surface
• Nonlinear Bosonization of Fermi Surfaces: The Method of Coadjoint Orbits
• Theory of Fermion Liquids
• Geometrical Approach to Bosonization of D>1 Dimensional (Non) Fermi Liquids
• Supersymmetric low-energy theory and renormalization group for a clean Fermi gas with a repulsion in arbitrary dimensions
• Bosonization for disordered and chaotic systems
• Temperature dependence of the spin susceptibility of a clean Fermi gas with repulsion
• The effect of Fermi surface curvature on low-energy properties of fermions with singular interactions
• Describing systems of interacting fermions by boson models: exact mapping in arbitrary dimension and applications
• An exact method for bosonizing the Fermi surface in arbitrary dimensions
• Searching for non-Fermi liquids under holographic light
• Exact solution of a 2D interacting fermion model
• Effective field theory of Berry Fermi liquid from the coadjoint orbit method
• Effective field theory for ersatz Fermi liquids
• Reckoning with the Mother of all non-Fermi liquids: alien bosonization vs predator holography
• Phase space holography with no strings attached
• Effective short distance interaction in Calogero-Sutherland quantum fluids
• Vertex corrections of impurity scattering at a ferromagnetic quantum critical point
• Fermi Surface Bosonization for Non-Fermi Liquids
• Collective mode description for a clean Fermi gas with repulsion in arbitrary dimensions: interaction of spin excitations and its consequences
• Critical theory of Pomeranchuk transitions via high-dimensional bosonization
• Bosonic Bogoliubov transformations as Lorentz boosts in $(c,\overline{c})=(1,1)$ conformal field theories with marginal $J\overline{J}$ deformations