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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 .
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.
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.
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
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}} ).
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 ...
This category is for mathematical identities, i.e. identically true relations holding in some area of algebra (including abstract algebra, or formal power series). Subcategories This category has only the following subcategory.
List of logarithmic identities; List of mathematical functions; List of mathematical identities; List of mathematical proofs; List of misnamed theorems; List of scientific laws; List of theories; Most of the results below come from pure mathematics, but some are from theoretical physics, economics, and other applied fields.