Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

I am puzzled by some lines I read in Mattuck's book on Feynman diagrams in many-body problems ( http://www.amazon.com/Feynman-Diagrams-Many-Body-Problem-Physics/dp/0486670473 ) Page 21 (1.14) for those who have the book. Basically after representing the full propagator of an electron in an electron gas by expansion of the electron-electron interaction (not specified but QED I guess), it says: "this is the 'Hartree-Fock' approximation for the electron gas", which I still don't understand. The Hartree-Fock method for me is just an iterative tool to calculate the collective wave-function of self-interacting fermions satisfying the correct anti-symmetrized form. This statement is evasive to me, and I'd like to understand in which way it makes sense.

share|improve this question
I don't have this book but I think "Hartree-Fock approximation" means that you consider only states that are slater determinants of one-electron states, i.e. electron-electron correlations are neglected. –  jjcale Nov 2 '12 at 18:10
Ok, and on what grounds do we neglect those correlations, it has always perturbed me that the use of a Slater determinant means complete separability between the electrons wave-functions without it being clearly justified. –  Learning is a mess Nov 4 '12 at 10:45
add comment

1 Answer

up vote 2 down vote accepted

These Feynman diagrams can be summed by solving the Dyson-Schwinger equation $$ G = G_0 + G_0\Sigma G $$ This is a self-consistency equation for $G$. Now write $G_0$ and $G$ in terms of single particle wave functions, $$ G(x,x';\omega)=\sum_j \phi_j(x)\phi^*_j(x')\left[ \frac{\Theta(E_j-E_F)}{\omega-E_j+i\epsilon} +\frac{\Theta(E_F-E_j)}{\omega-E_j-i\epsilon} \right]. $$ Then the Dyson-Schwinger equation becomes a coupled set of equations for the eigenfunctions $\phi_j$ and the eigenvalues $E_j$. These are the standard Hartee-Fock equations. This is explained in some detail in many text books, for example Negele and Orland, or Fetter and Walecka.

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.