Fermi surface volume of interacting systems
Three Fermion sumrules for interacting systems are derived at T=0, involving the number expectation N-bar (μ), canonical chemical potentials μ(m), a logarithmic time derivative of the Greens function γ{sub k-vector σ} and the static Greens function. In essence we establish at zero temperature the sumrules linking: N-bar (μ)↔∑{sub m}Θ(μ−μ(m))↔∑{sub k-vector ,σ}Θ(γ{sub k-vector σ})↔∑{sub k-vector ,σ}Θ(G{sub σ}( k-vector ,0)). Connecting them across leads to the Luttinger and Ward sumrule, originally proved perturbatively for Fermi liquids. Our sumrules are nonperturbative in character and valid in a considerably broader setting that additionally includes non-canonical Fermions and Tomonaga–Luttinger models. Generalizations are given for singlet-paired superconductors, where one of the sumrules requires a testable assumption of particle–hole symmetry at all couplings. The sumrules are found by requiring a continuous evolution from the Fermi gas, and by assuming a monotonic increase of μ(m) with particle number m. At finite T a pseudo-Fermi surface, accessible to angle resolved photoemission, is defined using the zero crossings of the first frequency moment of a weighted spectral function.