Related papers: Formal and Precise Derivation of the Green Functio…
We discuss the Hamiltonian formulation of the Schwinger proper-time method of calculating Green functions in gauge theories. Instead of calculating Feynman diagrams, we solve the corresponding Dyson-Schwinger equations. We express the…
The purpose of this paper is to investigate some spectral properties of Sturm-Liouville type problems with interior singularities. Some of the mathematical aspects necessary for developing own technique presented. By applying this technique…
Based on results of Digne-Michel-Lehrer (2003) we give two formulae for two-variable Green functions attached to Lusztig induction in a finite reductive group. We present applications to explicit computation of these Green functions, to…
We consider a fractional Laplace equation and we give a self-contained elementary exposition of the representation formula for the Green function on the ball. In this exposition, only elementary calculus techniques will be used, in…
Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image processing, and many analytic approaches or traditional…
In this study, we give the Sturm comparison theorems for discrete fractional Sturm-Liouville (DFSL) equations within Riemann-Liouville and Gr\"unwald-Letnikov sense. The emergence of Sturm-Liouville equations began as one dimensional…
In this work, we study the scattering problem of the general nonlinear finitely many Dirac delta potentials with complex coupling constants (or opacities in the context of optics) using the Green's function method and then find the bound…
We study classical binary fluid mixtures in which densities vary on very short time (ps) and length (nm) scales, such that hydrodynamics does not apply. In a pure fluid with a localized heat pulse the breakdown of hydrodynamics was overcome…
Based on the generating functional method with an external source function, a useful constraint on the source function is proposed for analyzing the one- and two-loop world-line Green functions. The constraint plays the same role as the…
A Green's function approach to the inclusive quasielastic ($e,e'$) scattering is presented. The components of the nuclear response are written in terms of the single-particle optical model Green's function. The explicit calculation of the…
We derive a variational formula for the outward normal derivative of the Green function for the Schr\"odinger and Laplace--Beltrami operators, viewed as perturbations of the Laplacian. As an application we begin to characterize elliptic…
We describe the computation of generalized Green functions and 2-parameter Green functions for finite reductive groups.
It is shown that the conventional many-body techniques to calculate the Green's functions can be applied to the wide, compressible edge of a quantum Hall bar. The only ansatz we need is the existence of stable density modes that yields a…
A explicit formula on semiclassical Green functions in mixed position and momentum spaces is given, which is based on Maslov's multi-dimensional semiclassical theory. The general formula includes both coordinate and momentum representations…
Strings propagating along surfaces with Dirichlet boundaries are studied in this paper. Such strings were originally proposed as a possible candidate for the QCD string. Our approach is different from previous ones and is simple and general…
The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and…
We present a new approach to real-space multiple-scattering theory for molecules and clusters, based on the two-potential (distorted-wave) Lippmann-Schwinger equation formalism. Our approach uses a recently developed form [D. L. Foulis,…
This paper provides a new analytical method to obtain Green's functions of linear dispersive partial differential equations. The Euler-Bernoulli beam equation and the one-dimensional heat conduction equation (dissipation equation) under…
Arakelov-Green functions defined on metrized graphs have important role in relating arithmetical problems on algebraic curves into graph theoretical problems. In this paper, we clarify the combinatorial interpretation of certain…
We introduce a general approach to traces that we consider as linear continuous functionals on some function space where we focus on some special choices for that space. This leads to an integral calculus for the computation of the precise…