A dyson equation approach to the calculation of correlation functions

Stefano Paggi

Raoul Rashidovich Nigmatullin

Chuanru Dai, Wenxin Ding

Abstract The essential difficulty of a large portion of the strongly interacting systems can be traced down to the “noncanonicality” of the underlying operators which are used to formulate the theory, like t-J model, Hubbard-type models in the large-U limit, quantum spin, etc. We proposed a new Schwinger-Dyson equations-of-motion method to compute the dynamical correlation functions of quantum spins at zero temperature. This method can also compute all the static observables from the dynamical correlation functions. We propose that this method can formulate dynamical perturbation calculations for quantum spin-1/2 models.

Jing-Min Hou, Li-Jun Tian

The Green's functions and the correlation functions in spin-2 Bose–Einstein condensates at finite temperature are defined and the generalized Dyson–Beliaev equations are introduced. We discuss the spin conservation in z direction and decouple the Green's functions and the generalized Dyson–Beliaev equations according to different spin conservations in z direction. The anomalous vertex functions are introduced and the self-energies are separated into the proper self-energies and the improper self-energies. The generalized Dyson–Beliaev equations are decoupled according to separation of the self-energies. We calculate the Green's functions step by step in the Bogoliubov approximation and discuss the collective excitations in spin-2 Bose–Einstein condensates in the polar, ferromagnetic, and cyclic cases, respectively.

Giorgio Parisi A

Hou, Jing-Min, Tian Tian +1 more

The Green's functions and the correlation functions in spin-2 Bose-Einstein condensates at finite temperature are defined and the generalized Dyson-Beliaev equations are introduced. We discuss the spin conservation in z direction and decouple thre Green's functions and the generalized Dyson-Beliaev equations according to different spin conservations in z direction. The anomalous vertex functions are introduced and the self-energies are separated into the proper self-energies and the improper self-energies. The generalized Dyson-Beliaev equations are decoupled according to separation of the self-energies. We calculate the Green's functions step by step in the Bogoliubov approximation and discuss the collective excitations in spin-2 Bose-Einstein condensates in the polar, ferromagnetic, and cyclic cases,respectively.