Related papers: Formulae for two-variable Green functions
We construct an explicit Green's function for the conjugated Laplacian $e^{-\omega \cdot x/h}\Delta e^{-\omega \cdot x/h}$, which let us control our solutions on roughly half of the boundary. We apply the Green's function to solve a partial…
We study the one-dimensional Schr\"odinger equation and derive exact expressions for the Green function in terms of reflection coefficients which are defined for semi-infinite intervals. We also discuss the relation between our results and…
Green functions play an important role in conformal geometry. In this paper, we explain how to compute explicitly the logarithmic singularities of the Green functions of the conformal powers of the Laplacian. These operators include the…
Closed expressions for the Green functions of the stationary two-dimensional two-component Schrodinger equation for an electron moving in monolayer and bilayer graphene in the presence of a magnetic field are obtained in terms of the…
We derive an exact closed-form representation for the Euclidean thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space. This can be interpreted as the real part of a complex analytic function of a…
Let W be the complex reflection group G(e,1,n). In the author's previous paper, Hall-Littlewood functions associated to W were introduced. In the special case where W is a Weyl group of type B_n, they are closely related to Green…
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 construct Green's function for second order elliptic operators of the form $Lu=-\nabla \cdot (\mathbf{A} \nabla u + \boldsymbol{b} u)+ \boldsymbol c \cdot \nabla u+ du$ in a domain and obtain pointwise bounds, as well as Lorentz space…
A first order differential equation of Green's Function, at the origin G(0), for the one- dimensional lattice is derived by simple recurrence relation. Green's Function at site (m)is then calculated in terms of G(0). A simple recurrence…
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…
We construct Green functions of conormal derivative problems for the stationary Stokes system with measurable coefficients in a two dimensional Reifenberg flat domain.
We derive a closed-form expression for the Green function of linear evolution equations with the Dirichlet boundary condition for an arbitrary region, based on the singular perturbation approach to boundary problems.
There are many applications in gauge theories where the usually employed framework involving gauge-dependent Green's functions leads to considerable problems. In order to overcome the difficulties invariably tied to gauge dependence, we…
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 study the full set of planar Green's functions for a two-matrix model using the language of functions of non-commuting variables. Both the standard Schwinger-Dyson equations and equations determining connected Green's functions can be…
The magnon Hedin's equations are derived via the Schwinger functional derivative technique, and the resulting self-consistent Green's function method is used to calculate ground state spin patterns and magnetic structure factors for…
A numerical method is developed for calculating the real time Green's functions of very large sparse Hamiltonian matrices, which exploits the numerical solution of the inhomogeneous time-dependent Schroedinger equation. The method has a…
In this paper we obtain an explicit formula of the parameter dependence of the partial derivatives of the Green's functions related to two-point boundary conditions. Such expression follows as an integral of both kernels times the…
We consider gauge invariant quark two-point Green's functions in which the gluonic phase factor follows a skew-polygonal line. Using a particular representation for the quark propagator in the presence of an external gluon field, functional…
We calculate the multipoint Green functions in 1+1 dimensional integrable quantum field theories. We use the crossing formula for general models and calculate the 3 and 4 point functions taking in to account only the lower nontrivial…