Monte Carlo Second- and Third-Order Many-Body Green’s Function Methods with Frequency-Dependent, Nondiagonal Self-Energy

2019 ◽  
Vol 15 (11) ◽  
pp. 6097-6110
Author(s):  
Alexander E. Doran ◽  
So Hirata
Keyword(s):  
Monte Carlo ◽  
Green’S Function ◽  
Green's Function ◽  
Many Body ◽  
Third Order ◽  
Frequency Dependent ◽  
Self Energy

Monte Carlo explicitly correlated many-body Green’s function theory

2018 ◽  
Vol 149 (17) ◽  
pp. 174112 ◽  
Author(s):  
Cole M. Johnson ◽  
Alexander E. Doran ◽  
Seiichiro L. Ten-no ◽  
So Hirata
Keyword(s):  
Monte Carlo ◽  
Green’S Function ◽  
Green's Function ◽  
Function Theory ◽  
Many Body ◽  
Explicitly Correlated

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.

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