Zero-temperature limit and statistical quasiparticles in many-body perturbation theory

TL;DR

This paper rigorously establishes the consistency of zero-temperature limit and statistical quasiparticles in many-body perturbation theory, ensuring thermodynamic relations hold at all orders for Fermi systems.

Contribution

It derives a thermodynamic perturbation series that confirms the consistency of zero-temperature formalism with statistical mechanics in Fermi liquids.

Findings

Proves thermodynamic relations hold at all orders in perturbation theory.

Establishes the connection between zero-temperature limit and statistical quasiparticles.

Validates the formalism for both isotropic and anisotropic Fermi systems.

Abstract

The order-by-order renormalization of the self-consistent mean-field potential in many-body perturbation theory for normal Fermi systems is investigated in detail. Building on previous work mainly by Balian and de Dominicis, as a key result we derive a thermodynamic perturbation series that manifests the consistency of the adiabatic zero-temperature formalism with perturbative statistical mechanics---for both isotropic and anisotropic systems---and satisfies at each order and for all temperatures the thermodynamic relations associated with Fermiliquid theory. These properties are proved to all orders.