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The general study of Green's function written in the above form, and its relationship to the function spaces formed by the eigenvectors, is known as Fredholm theory. There are several other methods for finding Green's functions, including the method of images, separation of variables, and Laplace transforms. [1]
In many-body theory, the term Green's function (or Green function) is sometimes used interchangeably with correlation function, but refers specifically to correlators of field operators or creation and annihilation operators. The name comes from the Green's functions used to solve inhomogeneous differential equations, to which they are loosely ...
The coherent potential approximation (CPA) is a method, in theoretical physics, of finding the averaged Green's function of an inhomogeneous (or disordered) system. The Green's function obtained via the CPA then describes an effective medium whose scattering properties represent the averaged scattering properties of the disordered system being approximated.
The Green's function to be used in the above integral is one which vanishes on the boundary: (,) = for and . Such a Green's function is usually a sum of the free-field Green's function and a harmonic solution to the differential equation.
This method is a specific application of Green's functions. [citation needed] The method of images works well when the boundary is a flat surface and the distribution has a geometric center. This allows for simple mirror-like reflection of the distribution to satisfy a variety of boundary conditions.
The GW approximation (GWA) is an approximation made in order to calculate the self-energy of a many-body system of electrons. [1] [2] [3] The approximation is that the expansion of the self-energy Σ in terms of the single particle Green's function G and the screened Coulomb interaction W (in units of =)
In quantum field theory, correlation functions, often referred to as correlators or Green's functions, are vacuum expectation values of time-ordered products of field operators. They are a key object of study in quantum field theory where they can be used to calculate various observables such as S-matrix elements.
Green's functions can be expanded in terms of the basis elements (harmonic functions) which are determined using the separable coordinate systems for the linear partial differential equation. There are many expansions in terms of special functions for the Green's function. In the case of a boundary put at infinity with the boundary condition ...