Quantum Field Theory of Correlated Bose-Einstein condensates: I. Basic Formalism

TL;DR

This paper develops a quantum field theoretical framework for Bose-Einstein condensates that respects fundamental physical principles and allows for the analysis of correlated condensates with gapless excitations across various conditions.

Contribution

It introduces a formalism based on irreducible vertices to study correlated Bose-Einstein condensates without infrared divergences, extending the Gavoret-Nozières results to finite temperature and nonequilibrium states.

Findings

Green's functions share poles, indicating persistent two-particle correlations.

The structure of two-particle Green's functions remains consistent across temperature and inhomogeneity.

The formalism satisfies conservation laws and Goldstone's theorem.

Abstract

Quantum field theory of equilibrium and nonequilibrium Bose-Einstein condensates is formulated so as to satisfy three basic requirements: the Hugenholtz-Pines relation; conservation laws; identities among vertices originating from Goldstone's theorem I. The key inputs are irreducible four-point vertices, in terms of which we derive a closed system of equations for Green's functions, three- and four-point vertices, and two-particle Green's functions. It enables us to study correlated Bose-Einstein condensates with a gapless branch of single-particle excitations without encountering any infrared divergence. The single- and two-particle Green's functions are found to share poles, i.e., the structure of the two-particle Green's functions predicted by Gavoret and Nozi\`eres for a homogeneous condensate at $T=0$ is also shown to persist at finite temperatures, in the presence of inhomogeneity, and also in nonequilibrium situations.