Related papers: Remarks on computing Green functions
It is shown that every Feynman integral can be interpreted as Green function of some linear differential operator with constant coefficients. This definition is equivalent to usual one but needs no regularization and application of…
We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation…
We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the…
We discuss in an introductory manner structural similarities between the polylogarithm and Green functions in quantum field theory.
We propose a multiloop generalization of the Bern-Kosower formalism, based on Strassler's approach of evaluating worldline path integrals by worldline Green functions. Those Green functions are explicitly constructed for the basic two-loop…
In this paper, we summarize the technique of using Green functions to solve electrostatic problems. We start by deriving the electric potential in terms of a Green function and a charge distribution. We then provide a variety of example…
The hierarchy of Green functions for (quasi)degenerate systems, presented in cond-mat/0308058, is calculated in detail for the case of a system with closed shells plus a single electron in a two-fold degenerate level. The complete hierarchy…
This is a compendium of generating functions involving single, double sums and definite integrals. These generating functions also involve special functions in both the summand function and closed form solution.
We study several quantities associated to the Green's function of a multiply connected domain in the complex plane. Among them are some intrinsic properties such as geodesics, curvature, and $L^2$-cohomology of the capacity metric and…
Green's functions are highly useful in analyzing the dynamical behavior of polynomials in their escaping set. The aim of this paper is to construct an analogue of Green's functions for planar quasiregular mappings of degree two and constant…
We give defining equations for function fields over finite fields with many rational places. They are obtained from composita of quadratic extensions of the rational function field.
We construct the Green function for second order elliptic equations in non-divergence form when the mean oscillations of the coefficients satisfy the Dini condition and the domain has $C^{1,1}$ boundary. We also obtain pointwise bounds for…
Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum…
Minimal representations of a real reductive group G are the `smallest' irreducible unitary representations of G. We discuss special functions that arise in the analysis of L^2-model of minimal representations.
A method for the computation of scattering data and of the Green function for the one-dimensional Schr\"{o}dinger operator $H:=-\frac{d^2}{dx^2}+q(x)$ with a decaying potential is presented. It is based on representations for the Jost…
Using the Gegenbauer polynomials and the zonal harmonics functions we give some representation formula of the Green function in the annulus. We apply this result to prove some uniqueness results for some nonlinear elliptic problems.
In this paper we study the gradient estimate for positive solutions of Schrodinger equations on locally finite graph. Then we derive Harnack's inequality for positive solutions of the Schrodinger equations. We also set up some results about…
Aggregation functions are generally defined and used to combine several numerical values into a single one, so that the final result of the aggregation takes into account all the individual values in a given manner. Such functions are…
We give a generalisation of the character formula of Deligne--Lusztig representations from the finite field case to the truncated formal power series case. Motivated by this generalisation, we give a definition of Green functions for these…
We explicitly calculate the Green functions describing quantum changes of topology in Friedman-Lemaitre-Robertson-Walker Universes whose spacelike sections are compact but endowed with distinct topologies. The calculations are performed…