Quantum Field Theory of Correlated Bose-Einstein condensates: II. Ward-Takahashi Identities and Correlation Functions

Abstract

We derive Ward-Takahashi identities for correlated Bose-Einstein condensates based on the expressions of the first-order variations $(\delta \Psi ,\delta G)$ due to perturbations obtained in the preceding paper [T. Kita, J. Phys. Soc. Jpn. $90$, 024001 (2021)] for the condensate wave function $\Psi$ and Green's function $G$. They enable us to obtain several exact results on the density and current correlation functions $K_{\nu {\nu }^{\prime }}^{}$, and also express $K_{\nu {\nu }^{\prime }}^{}$ in terms of low-energy Green's functions and vertices. The latter expressions open up the possibility of constructing theory of superfluid Bose liquids in the same way as that for fermions at low temperatures. The vertices are found to have different limits depending on which of frequency $\omega$ and wavenumber $q$ is set equal to zero first.

11 pages

References in corpus (4)

• A Renormalization-Group Study of Interacting Bose-Einstein condensates: Absence of the Bogoliubov Mode below Four ($T>0$) and Three ($T=0$) Dimensions
• Strong connection between single-particle and density excitations in Bose-Einstein condensates
• Quantum Field Theory of Correlated Bose-Einstein condensates: I. Basic Formalism
• A Renormalization-Group Study of Interacting Bose-Einstein Condensates: II. Anomalous Dimension $\eta$ for $d\lesssim 4$ at Finite Temperatures

Cited by in corpus (2)

• Quantum Field Theory of Correlated Bose-Einstein condensates: I. Basic Formalism
• Hidden Bose-Einstein Singularities in Correlated Electron Systems: II. Pseudogap Phase in the Weakly Attractive Hubbard Model