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In mathematics, Green's identities are a set of three identities in vector calculus relating the bulk with the boundary of a region on which differential operators act. They are named after the mathematician George Green , who discovered Green's theorem .
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.
In mathematics, Green formula may refer to: Green's theorem in integral calculus; Green's identities in vector calculus; Green's function in differential equations; the Green formula for the Green measure in stochastic analysis
This article lists mathematical identities, that is, identically true relations holding in mathematics. Bézout's identity (despite its usual name, it is not, properly speaking, an identity) Binet-cauchy identity
Also, Green's functions in general are distributions, not necessarily functions of a real variable. Green's functions are also useful tools in solving wave equations and diffusion equations. In quantum mechanics, Green's function of the Hamiltonian is a key concept with important links to the concept of density of states.
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In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in ) bounded by C. It is the two-dimensional special case of Stokes' theorem (surface in R 3 {\displaystyle \mathbb {R} ^{3}} ).
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