Effective integral equation and vertex operator of the green function

T. Lukes, M. Roberts

Roland K. Wehner

Abstract The time‐ordered many‐time Green functions are studied for a general lattice Hamiltonian which includes effects of a static electric field and of homogeneous deformations. The structure of the self‐energy part is investigated, and integral equations are derived for a cubic and a quartic vertex part.

Famous Akpojotor, Ejiroghene G. Akpojotor, Lawrence Atuma

We calculated the exact self energy and the exact Green's function for the Bethe lattice in the hopping model using the Dyson's equation and from the fourth order of perturbation theory. The self energy is found from processes where an electron hops to its neighbors and includes terms where the particle hops twice to a next nearest neighbor (NNN) and then hops back. carried out by counting all non-self intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice, the same equation is obtained from a path integral approach for the partition function. In this study, the electron Green's function will be used to calculate the exact Green's function and self energy for the Bethe lattice in the hopping model. Though it is not one of the goals of our study here, it is pertinent to point out that the self energy can be used to obtain the vertex function which contains all the information on the kinetic and interaction behaviour of the particles in the system. Interestingly the vertex function can be decoupled into the charge vertex function and spin vertex function, thereby enabling the studying of either non-spin ordering systems or spin ordering system independently.

e.H. Hellal

Clas Blomberg

S. Y. Tsay Tzeng, T.T.S. Kuo, Yiharn Tzeng +2 more

In conventional Green's function methods the vertex function \ensuremath{\Gamma} is generally energy dependent. However, a model-space Green's function method where the vertex function is manifestly energy independent can be formulated using energy-independent effective interaction theories based on folded diagrams and/or similarity transformations. This is discussed in general and then illustrated for a 1p1h model-space Green's function applied to a solvable Lipkin many-fermion model. The poles of the conventional Green's function are obtained by solving a self-consistent Dyson equation and model space calculations may lead to unphysical poles. For the energy-independent model-space Green's function only the physical poles of the model problem are reproduced and are in satisfactory agreement with the exact excitation energies. \textcopyright{} 1996 The American Physical Society.