Related papers: Underdetermined Dyson-Schwinger equations
We consider some non-linear non-homogeneous partial differential equations (PDEs) and derive their exact Green function solution as a functional Taylor expansion in powers of the source. The kind of PDEs we consider are dispersive ones…
The question of which non-interacting Green's function "best" describes an interacting many-body electronic system is both of fundamental interest as well as of practical importance in describing electronic properties of materials in a…
Parameters of differential equations are essential to characterize intrinsic behaviors of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for…
We develop the discrete set of Dyson-Schwinger equations for scalar fields and solve them for some cases. We show that their solutions are Gaussian in the continuum limit as expected from the theorems of Aizenman and of Aizenman and…
In this study, we address the challenge of obtaining a Green's function operator for linear partial differential equations (PDEs). The Green's function is well-sought after due to its ability to directly map inputs to solutions, bypassing…
Two examples of recent progress in applications of the Dyson-Schwinger equation (DSE) formalism are presented: (1) Strong coupling quantum electrodynamics in 4 dimensions (QED$_4$) is an often studied model, which is of interest both in its…
We present a new method for calculating the Green functions for a lattice scalar field theory in $D$ dimensions with arbitrary potential $V(\phi)$. The method for non-perturbative evaluation of Green functions for $D \! = \! 1$ is…
In calculating Green functions for interacting quantum systems numerically one often has to resort to finite systems which introduces a finite size level spacing. In order to describe the limit of system size going to infinity correctly,…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
Calculations of excited states in Green's function formalism often invoke the diagonal approximation, in which the quasiparticle states are taken from a mean-field calculation. Here, we extend the stochastic approaches applied in the…
We summarise recent results on the properties of gluons, quarks and light mesons from the Green's functions approach to QCD. We discuss a self-consistent, infrared power law solution for the Schwinger-Dyson equations of the 1PI-Greens…
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 obtained by iterating a set of functional differential equations…
Calculations of ground-state and excited-state properties of materials have been one of the major goals of condensed matter physics. Ground-state properties of solids have been extensively investigated for several decades within the…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
A new approximation scheme for non-perturbative calculations in a quantum field theory is proposed. The scheme is based on investigation of solutions of the Schwinger equation with its singular character taken into account. As a necessary…
A new approach proposed recently by author for the calculation of Green functions in quantum field theory and quantum mechanics is briefly reviewed. The method is applied to nonperturbative calculations for anharmonic oscillator,…
We compare the solutions of one-scale Dyson-Schwinger equations in the Minimal subtraction (MS) scheme to the solutions in kinematic (MOM) renormalization schemes. We establish that the MS-solution can be interpreted as a MOM-solution, but…
Analytic continuations of integer-valued parameters can lead to profound insights, such as angular momentum in Regge theory, the number of replicas in spin glasses, the number of internal degrees of freedom, the spacetime dimension in…
Single-particle resonances are crucial for exotic nuclei near and beyond the drip lines. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold becomes very important and can lead…
The real-time contour formalism for Green's functions provides time-dependent information of quantum many-body systems. In practice, the long-time simulation of systems with a wide range of energy scales is challenging due to both the…