Statistical Physics, Part 2

atoms axis Bose liquid calculate chemical potential coefficient commutation condensate condition constant coordinates correlation function corresponding crystal d³x definition denote density dependence derivative determined diagram technique distances electron elementary excitations energy spectrum equation expansion expressed in terms external field external lines factor Fermi gas Fermi liquid Fermi surface ferromagnet fluctuations formula Fourier components free energy given gives Green's function Hamiltonian Heisenberg Hence integrand integration with respect interaction k₂ lattice limit linear macroscopic magnetic field magnetic moment magnon matrix elements medium metal momenta momentum motion non-zero number of particles obtain operator P₁ pair parameter perturbation theory phase phonon pole problem properties quantum quasi-momentum quasi-particle r₁ relation replaced representation result solution spin Substituting suffix summation superconductivity superfluid temperature tensor tion transition variable vector velocity vertex function volume vortex filament wave function zero