Related papers: Global Hadamard form for the Green Function in Sch…
In this paper, we consider band-structure calculations governed by the Helmholtz or Maxwell equations in piecewise homogeneous periodic materials. Methods based on boundary integral equations are natural in this context, since they…
In this work we have presented a rather general and easy-to-apply method for discrete Hilbert space representation of quantum mechanical Green's operators. We have shown that if in some discrete Hilbert space basis representation the…
We study the radial flow of retarded Green's function of energy-momentum tensor and $R$-current of dual gauge theory in presence of generic higher derivative terms in bulk Lagrangian. These are first order non-linear Riccati equations. We…
We study the Laplacian on Stenzel spaces (generalized deformed conifolds), which are tangent bundles of spheres endowed with Ricci flat metrics. The (2d-2)-dimensional Stenzel space has SO(d) symmetry and can be embedded in C^d through the…
We construct Hadamard states for the Yang-Mills equation linearized around a smooth, space-compact background solution. We assume the spacetime is globally hyperbolic and its Cauchy surface is compact or equal $\rr^d$. We first consider the…
Using the gravity side of the AdS/CFT correspondence, we investigate the analytic properties of thermal retarded Green's functions for scalars, conserved currents, the stress tensor, and massless fermions. We provide some results concerning…
In this paper we analyze the vacuum expectation values of the field squared and the energy-momentum tensor associated to a massive scalar field in a higher dimensional cosmic string spacetime, obeying Dirichlet or Neumann boundary…
We show that an analogue of the (four dimensional) image sum method can be used to reproduce the results, due to Krasnikov, that for the model of a real massless scalar field on the initial globally hyperbolic region IGH of two-dimensional…
We prove that the singularity structure of all n-point distributions of a state of a generalised real free scalar field in curved spacetime can be estimated if the two-point distribution is of Hadamard form. In particular this applies to…
The pointwise space-time behavior of the Green's function of the one-dimensional Vlasov-Maxwell-Boltzmann (VMB) system is studied in this paper. It is shown that the Green's function consists of the macroscopic diffusive waves and Huygens…
Recent work in the literature has studied rigid Casimir cavities in a weak gravitational field, or in de Sitter spacetime, or yet other spacetime models. The present review paper studies the difficult problem of direct evaluation of scalar…
This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by "locally-rough surfaces" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary…
In absence of explicit solutions of the perturbation equation of a static symmetrical homogeneous space-time, the best we can do is to construct a {\it quasi-}transformation. In this framework, we solve the perturbation equation with…
In this short note, we present the sharp estimate for the existence of a unique solution for a Hadamard-type fractional differential equations with two-point boundary value conditions. The method of analysis is obtained by using the…
By introducing multipe-site correlation functions, we propose a hierarchical Green function approach, and apply it to study the characteristic properties of a 2D square lattice Hubbard model by solving the equation of motions of a…
Applications of the H\"uckel (tight binding) model are ubiquitous in quantum chemistry and solid state physics. The matrix representation of this model is isomorphic to an unoriented vertex adjacency matrix of a bipartite graph, which is…
Motivated by the desire to test modified gravity theories exhibiting the Vainshtein mechanism, we solve in various physically relevant limits, the retarded Galileon Green's function (for the cubic theory) about a background sourced by a…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
Inspired by a result of Colding, the present paper studies the Green function $G$ on a non-parabolic $\mathrm{RCD}(0,N)$ space $(X, \mathsf{d}, \mathfrak{m})$ for some finite $N>2$. Defining $\mathsf{b}_x=G(x, \cdot)^{\frac{1}{2-N}}$ for a…
Equal-time Green's function is used to derive a three-dimensional integral equation from the Bethe-Salpeter equation. The resultant equation, in the absence of anti-particles, is identical to the use of time-ordered diagrams, and has been…