Many-body theory is largely based on self-consistent equations that are constructed in terms
of the physical quantity of interest itself, for example the density. Therefore, the calculation of …

Several widely used methods for the calculation of band structures and photo emission
spectra, such as the GW approximation, rely on many-body perturbation theory. They can be …

In this work we determine the one-body Greenʼs function as solution of a set of functional
integro-differential equations, which relate the one-particle Greenʼs function to its functional …

We show that the equations underlying the GW approximation have a large number of
solutions. This raises the question, how can we find the physical solution? We provide two …

It is shown that, in d-dimensional systems, the vertex corrections beyond the random phase
approximation (RPA) or GW approximation scales with the power d− β− α of the Fermi …

In a typical scenario the diagrammatic many-body perturbation theory generates asymptotic
series. Despite non-convergence, the asymptotic expansions are useful when truncated to a …

We present a formal derivation of the many-body perturbation theory for a system of
electrons and bosons subject to a nonlinear electron-boson coupling. The interaction is …

We consider a self-convolutive recurrence whose solution is the sequence of coefficients in
the asymptotic expansion of the logarithmic derivative of the confluent hypergeometric …

Many-body perturbation theory is often formulated in terms of an expansion in the dressed
instead of the bare Green's function, and in the screened instead of the bare Coulomb …

We consider a number of questions regarding the Luttinger-Ward functional and the many-
body perturbation series expansion of the proper self-energy $\Sigma (\mathbf {k}; z) …