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

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 Nozières 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.

12 pages, 2 figures

References in corpus (4)

• Effective action for Bose-Einstein condensates
• A Renormalization-Group Study of Interacting Bose-Einstein condensates: Absence of the Bogoliubov Mode below Four ($T>0$) and Three ($T=0$) Dimensions
• A Renormalization-Group Study of Interacting Bose-Einstein Condensates: II. Anomalous Dimension $\eta$ for $d\lesssim 4$ at Finite Temperatures
• Quantum Field Theory of Correlated Bose-Einstein condensates: II. Ward-Takahashi Identities and Correlation Functions

Cited by in corpus (2)

• Quantum Field Theory of Correlated Bose-Einstein condensates: II. Ward-Takahashi Identities and Correlation Functions
• How Infrared Singularities Affect Nambu-Goldstone Bosons at Finite Temperatures