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Hamilton–Jacobi–Einstein equation : ウィキペディア英語版
Hamilton–Jacobi–Einstein equation

In general relativity, the Hamilton–Jacobi–Einstein equation (HJEE) or Einstein–Hamilton–Jacobi equation (EHJE) is an equation in the Hamiltonian formulation of geometrodynamics in superspace, cast in the "geometrodynamics era" around the 1960s, by A. Peres in 1962 and others. It is an attempt to reformulate general relativity in such a way that it resembles quantum theory within a semiclassical approximation, much like the correspondence between quantum mechanics and classical mechanics.
It is named for Albert Einstein, Carl Gustav Jacob Jacobi, and William Rowan Hamilton. The EHJE contains as much information as all ten Einstein field equations (EFEs). It is a modification of the Hamilton–Jacobi equation (HJE) from classical mechanics, and can be derived from the Einstein–Hilbert action using the principle of least action in the ADM formalism.
==Background and motivation==


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