相关论文: What is the trouble with Dyson--Schwinger equation…
Linear free field theories are one of the few Quantum Field Theories that are exactly soluble. There are, however, (at least) two very different languages to describe them, Fock space methods and the Schroedinger functional description. In…
In these lectures I discuss Hopf algebras and Dyson-Schwinger equations. The lectures start with an introduction to Hopf algebras, followed by a review where Hopf algebras occur in particles physics. The final part of these lectures is…
Polygonal lines are used for the paths of the gluon field phase factors entering in the definition of gauge invariant quark Green's functions. This allows classification of the Green's functions according to the number of segments the…
The heavy quark sector of Coulomb gauge QCD is investigated, by making a heavy quark mass expansion of the QCD action and restricting to the leading order. With the truncation of the Yang-Mills sector to include only dressed two-point…
Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain simple representations for the Green's function of the Dirac-Oscillator and Dirac-Coulomb problems. This is accomplished…
Gauge theories have been a cornerstone of the description of the world at the level of the fundamental particles. The Lagrangian or the action describing the corresponding interactions is invariant under certain gauge transformations. This…
The well-known Green's function method has been recently generalized to nonlinear second order differential equations. In this paper we study possibilities of exact Green's function solutions of nonlinear differential equations of higher…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…
This paper examines the effectiveness of the Dyson-Schwinger (DS) equations as a calculational tool in quantum field theory. The DS equations are an infinite sequence of coupled equations that are satisfied exactly by the connected Green's…
An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the…
The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible…
We perform comparative analyses of quantum loop corrections to some observationally important two- and three-point Green functions within two distinct symmetry-breaking mechanisms. It appears that the existing high-energy data, neutrino…
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…
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 present the Green's functions that are the solutions of the massive Klein-Gordon equation for a scalar field with non-minimal coupling to gravitation for several static and expanding cosmological models. An important feature of such…
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…
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations)…
The Green's function method which has been originally proposed for linear systems has several extensions to the case of nonlinear equations. A recent extension has been proposed to deal with certain applications in quantum field theory. 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…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…