Related papers: Log-Expansions from Combinatorial Dyson-Schwinger …
Dyson-Schwinger equations determine the Green functions $G^r(\alpha,L)$ in quantum field theory. Their solutions are triangular series in a coupling constant $\alpha$ and an external scale parameter $L$ for a chosen amplitude $r$, with the…
Green functions in a quantum field theory can be expanded as bivariate series in the coupling and a scale parameter. The leading logs are given by the main diagonal of this expansion, i.e. the subseries where the coupling and the scale…
Dyson-Schwinger equations are integral equations in quantum field theory that describe the Green functions of a theory and mirror the recursive decomposition of Feynman diagrams into subdiagrams. Taken as recursive equations, the…
Using a general-order ab initio many-body Green's function method, we numerically illustrate several pathological behaviors of the Feynman-Dyson diagrammatic perturbation expansion of one-particle many-body Green's functions as electron…
We introduce a combinatorial version Mori-Zwanzig theory and develop from it a family of self-consistent evolution equations for the correlation function or Green's function of interactive many-body systems. The core idea is to use an…
We show how to use the Hopf algebra structure of quantum field theory to derive nonperturbative results for the short-distance singular sector of a renormalizable quantum field theory in a simple but generic example. We discuss renormalized…
We discuss similarities and differences between Green Functions in Quantum Field Theory and polylogarithms. Both can be obtained as solutions of fixpoint equations which originate from an underlying Hopf algebra structure. Typically, the…
Quantization of electrodynamics in curved space-time in the Lorenz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of non-minimal operators with variable coefficients. Starting from the integral…
We examine the relationship between three approaches (Hadamard, DeWitt-Schwinger and adiabatic) to the renormalization of expectation values of field operators acting on a charged quantum scalar field. First, we demonstrate that the…
The Dyson-Schwinger (DS) equations for a quantum field theory in $D$-dimensional space-time are an infinite sequence of coupled integro-differential equations that are satisfied exactly by the Green's functions of the field theory. This…
Quantization of electrodynamics in curved space-time in the Lorenz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of non-minimal operators with variable coefficients. Starting from the integral…
We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
We consider Schr\"odinger equations and Fokker-Planck equations in one dimension, and study the low-energy asymptotic behavior of the Green function using a new method. In this method, the coefficient of the expansion in powers of the wave…
We study low-energy expansion and high-energy expansion of reflection coefficients for one-dimensional Schr\"odinger equation, from which expansions of the Green function can be obtained. Making use of the equivalent Fokker-Planck equation,…
We generate the perturbative expansion of the single-particle Green's function and related self-energy for a half-filled single-band Hubbard model on a square lattice. We invoke algorithmic Matsubara integration to evaluate single-particle…
In a recent work the Green's functions of the $\mathcal{PT}$-symmetric scalar theory $g \phi^{2}(i\phi)^\epsilon$ were calculated at the first order of the logarithmic expansion, i.e. at first order in $\epsilon$, and it was proposed to use…
Most currently used approximations for the one-particle Green's function G in the framework of many-body perturbation theory, such as Hedin's GW approximation or the cumulant GW+C approach, are based on a linear response approximation for…
Coulomb gauge Yang-Mills theory within the first order formalism is considered with a view to deriving the propagator Dyson-Schwinger equations. The first order formalism is studied with special emphasis on the BRS invariance and it is…
The Feynman diagrams of the Green's function expansion of fermions interacting with a non-relativistic 2-body interaction are displayed in first, second and third order of the interaction as 2, 10 and 74 diagrams, respectively. A name…
Based on a canonical approach and functional-integration techniques, a series expansion of Green's function of a scalar field, in the presence of a medium, is obtained. A series expansion for Lifshitz-energy, in finite-temperature, in terms…