Related papers: Dyson-Schwinger equations in zero dimensions and p…
We present the construction and stochastic summation of rooted-tree diagrams, based on the expansion of a root finding algorithm applied to the Dyson-Schwinger equations (DSEs). The mathematical formulation shows superior convergence…
We provide a full and unbiased solution to the Dyson-Schwinger equation illustrated for $\phi^4$ theory in 2D. It is based on an exact treatment of the functional derivative $\partial \Gamma / \partial G$ of the 4-point vertex function…
In this work we present a numerical method to solve the set of Dyson-like equations arising the context of non-equilibrium Green's functions. The technique is based on the self-consistent solution of the Dyson equations for the interacting…
The Schwinger-Dyson equations connecting free and full Green functions and vertex parts widely were used in QED for finding full Green functions under different conditions. Undoubtedly, the same approach should leads to derivation of many…
We study the zero-dimensional prototype of the path integrals in quantum mechanics and quantum field theory, with the action $S(\phi)=\frac{\sigma }{2}\phi^{2}+\frac{\lambda}{4}\phi^{4}$. Using the Lefschetz thimble decomposition and the…
We study exact solutions of Dirac and Klein-Gordon equations and Green functions in d-dimensional QED and in an external electromagnetic field with constant and homogeneous field invariants. The cases of even and odd dimensions are…
Although nonperturbative functional methods are often associated with low energy Quantum Chromodynamics, contemporary studies indicate that they provide reliable tools to characterize a much wider spectrum of strongly interacting many-body…
Using simple models in D=0+0 and D=0+1 dimensions we construct partition functions and compute two-point correlations. The exact result is compared with saddle-point approximation and solutions of Schwinger-Dyson equations. When integrals…
We revisit the solution to the Schwinger-Dyson equations in the simple case of the 0-dimensional $\frac{1}{2}m^2 \phi^2 +\frac{\lambda}{4} \phi^4$ theory with $m^2>0$ and $\lambda \geq 0$. We argue that the truncated Schwinger-Dyson…
The stationary 1D Schr\"odinger equation with a polynomial potential $V(q)$ of degree N is reduced to a system of exact quantization conditions of Bohr-Sommerfeld form. They arise from bilinear (Wronskian) functional relations pairing…
In many ways the solution to the Hedin equations represents an exact solution to the many body problem. However, for most systems of practical interest, the solution to the Hedin equations is rendered nearly numerically intractable because…
We investigate the non-perturbative degrees of freedom in the class of non-local Higgs theories that have been proposed as an ultraviolet completion 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite…
We present a comprehensive study for common second order PDE's in two dimensional disk-like systems and show how their solution can be approximated by finding the Green function of an effective one dimensional system. After elaborating on…
We solve exactly the Dyson-Schwinger equations for Yang-Mills theory in 3 and 4 dimensions. This permits us to obtain the exact correlation functions till order 2. In this way, the spectrum of the theory is straightforwardly obtained and…
Unlike scalar and gauge field theories in four dimensions, gravity is not perturbatively renormalizable and as a result perturbation theory is badly divergent. Often the method of choice for investigating nonperturbative effects has been…
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…
For certain quantum field theories, the Kreimer-Connes Hopf-algebraic approach to renormalization reduces the Dyson-Schwinger equations to a system of non-linear ordinary differential equations for the expansion coefficients of the…
Shell corrections of the finite deformed Woods-Saxon potential are calculated using the Green's function method and the generalized Strutinsky smoothing procedure. They are compared with the results of the standard prescription which are…
Consider an $s$-dimensional function being evaluated at $n$ points of a low discrepancy sequence (LDS), where the objective is to approximate the one-dimensional functions that result from integrating out $(s-1)$ variables. Here, the…
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…