Theory of many-fermion systems

摘要: A general field-theoretical description of many-fermion systems, with or without quenched disorder, is developed. Starting from the Grassmannian action for interacting fermions, we first bosonize theory by introducing composite matrix variables that correspond to two-fermion excitations and integrating out fermion degrees freedom. The saddle point solution resulting field reproduces a disordered Hartree-Fock approximation an expansion Gaussian order about corresponds RPA-like theory. In clean limit they reduce ordinary random-phase approximations. We concentrate on perform symmetry analysis allows systematic separation massless modes massive ones. By treating in simple approximation, one obtains technically satisfactory derivation generalized nonlinear sigma-model has been used metal-insulator transitions. also treatment other phase transitions Fermi liquid. further use renormalization group techniques establish existence Fermi-liquid fixed point, show it stable all dimensions d>2. so-called weak-localization effects can be understood as corrections scaling near this point. studying limit. For case develop loop powers screened Coulomb interaction, represents improvement over RPA. corroborate d>1, agreement recent treatments liquids.