Self-energy, propagator

Corrections to the zeroth-order, inverse propagator in equation 26 are gathered together in a term known as the self-energy matrix, E(E). The Dyson equation may be written as... 

In this section, we describe our model, and give a brief, self-contained account on the equations of the non-equilibrium Green function formalism. This is closely related to the electron and particle-hole propagators, which have been at the heart of Jens electronic structure research [7,8]. For more detailed and more general analysis, see some of the many excellent references [9-15]. We restrict ourselves to the study of stationary transport, and work in energy representation. We assume the existence of a well-defined self-energy. The aim is to solve the Dyson and the Keldysh equations for the electronic Green functions ... 

The reducible part of AEgE)Wf, he-, the part of the diagram Fig. 1, (c) and (e), with the external state present in the propagator between the self-energy loop and the magnetic interaction, is given by [30,32]... 

The formal solution of (A. 17) requires, in each case, the inversion of (Qz — QHQ) 1, very often as complicated as that of z — H. However, when QHQ inverts easily, (A.17) provides the desired solution directly. Another important advantage of (A.17) is the possibility of a perturbative expansion when PHQ is small relative to the eigenterms of each subspace PHP and QHQ Then the third term of (A.17) is the self-energy associated with the propagation in P. 

In the subsequent discussion we shall need the irreducible 2- and 3-point functions i.e. the electron self energy Sy(p), the vacuum polarisation /7k,pv( ) and the full vertex function rv, PuP2% as knowledge of I vip) and determines the corresponding propagators Gy(p) and Dk,mv( ) completely and fy. iPuPz) represents the perturbative corrections to the free vertex The connection between these quantities is established by the Dyson equations (see e.g. [26])... 

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