Difficulty in the Method of Green's Functions for a Many-Body System

1962 ◽  
Vol 8 (9) ◽  
pp. 372-375 ◽  
Author(s):  
R. Balian ◽  
L. H. Nosanow ◽  
N. R. Werthamer
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Body System ◽  
Many Body

Difficulty in the Method of Green's Functions for a Many-Body System

1962 ◽  
Vol 8 (11) ◽  
pp. 466-466
Author(s):  
R. Balian ◽  
L. H. Nosanow ◽  
N. R. Werthamer
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Body System ◽  
Many Body

AN INTRODUCTORY GUIDE TO GREEN’S FUNCTION METHODS IN NUCLEAR MANY-BODY PROBLEMS

1994 ◽  
Vol 03 (02) ◽  
pp. 523-589 ◽  
Author(s):  
T.T.S. KUO ◽  
YIHARN TZENG
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Model Space ◽  
Many Body ◽  
Diagram Expansion ◽  
Nucleus Scattering ◽  
Many Body Systems ◽  
General Method

We present an elementary and fairly detailed review of several Green’s function methods for treating nuclear and other many-body systems. We first treat the single-particle Green’s function, by way of which some details concerning linked diagram expansion, rules for evaluating Green’s function diagrams and solution of the Dyson’s integral equation for Green’s function are exhibited. The particle-particle hole-hole (pphh) Green’s function is then considered, and a specific time-blocking technique is discussed. This technique enables us to have a one-frequency Dyson’s equation for the pphh and similarly for other Green’s functions, thus considerably facilitating their calculation. A third type of Green’s function considered is the particle-hole Green’s function. RPA and high order RPA are treated, along with examples for setting up particle-hole RPA equations. A general method for deriving a model-space Dyson’s equation for Green’s functions is discussed. We also discuss a method for determining the normalization of Green’s function transition amplitudes based on its vertex function. Some applications of Green’s function methods to nuclear structure and recent deep inelastic lepton-nucleus scattering are addressed.

scholarly journals Exceptional band touching for strongly correlated systems in equilibrium

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Tsuneya Yoshida ◽  
Robert Peters ◽  
Norio Kawakami ◽  
Yasuhiro Hatsugai
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Strongly Correlated Systems ◽  
Strongly Correlated ◽  
Many Body ◽  
Band Structures ◽  
Correlated Systems ◽  
Concise Review ◽  
Open Questions ◽  
Many Body Systems

Abstract Quasi-particles described by Green‘s functions of equilibrium systems exhibit non-Hermitian topological phenomena because of their finite lifetime. This non-Hermitian perspective on equilibrium systems provides new insights into correlated systems and attracts much interest because of its potential to solve open questions in correlated compounds. We provide a concise review of the non-Hermitian topological band structures for quantum many-body systems in equilibrium, as well as their classification.

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