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Find the Green's function for the following problem, whose Green's function number is X11: = ″ + = () =, = First step: The Green's function for the linear operator at hand is defined as the solution to
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 ...
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 ...
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.
The Green's function, (~ ~ ′), for the d'Alembertian is defined by the equation (~ ~ ′) = (~ ~ ′)where (~ ~ ′) is the multidimensional Dirac delta function ...
In his paper "The S-Matrix in Quantum electrodynamics", [1] Dyson derived relations between different S-matrix elements, or more specific "one-particle Green's functions", in quantum electrodynamics, by summing up infinitely many Feynman diagrams, thus working in a perturbative approach.
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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.