Quantum Many-particle Systems

analogous annihilation operators auxiliary field Bosons boundary conditions calculate classical consider contribution corresponding defined denote density derived dimension eigenstates eigenvalue equation evaluate evolution operator example expansion external Fermi surface Fermions Feynman diagrams finite temperature fluctuations Fourier functional integral Gaussian graphs Green's function ground state energy Hamiltonian Hartree Hartree-Fock Hence infinitesimal interaction labeled diagram Landau function magnetization many-body matrix element mean field mode momentum non-interacting notation Note obtain one-body one-particle order parameter particle partition function path integral permutation perturbation theory Phys physical poles potential Problem propagators quadratic quantum quasiparticle response function result ring diagrams sample second order Section single-particle Slater determinant spin stationary phase approximation stationary solutions stationary-phase approximation symmetry factor thermodynamic time-dependent time-ordered trajectory transform two-body variables vertex function wave function Wick's theorem yields zero sound zero temperature