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In physics, canonical quantum gravity is an attempt to quantize the canonical formulation of general relativity (or canonical gravity). It is a Hamiltonian formulation of Einstein's general theory of relativity. The basic theory was outlined by Bryce DeWitt in a seminal 1967 paper, and based on earlier work by Peter G. Bergmann using the so-called canonical quantization techniques for constrained Hamiltonian systems invented by Paul Dirac. Dirac's approach allows the quantization of systems that include gauge symmetries using Hamiltonian techniques in a fixed gauge choice. Newer approaches based in part on the work of DeWitt and Dirac include the Hartle–Hawking state, Regge calculus, the Wheeler–DeWitt equation and loop quantum gravity. == Canonical quantization == In the Hamiltonian formulation of ordinary classical mechanics the Poisson bracket is an important concept. A "canonical coordinate system" consists of canonical position and momentum variables that satisfy canonical Poisson-bracket relations, where the Poisson bracket is given by :, . These equations describe a ``flow" or orbit in phase space generated by the Hamiltonian . Given any phase space function , we have In canonical quantization the phase space variables are promoted to quantum operators on a Hilbert space and the Poisson bracket between phase space variables is replaced by the canonical commutation relation: In the so-called position representation this commutation relation is realized by the choice: and The dynamics are described by Schrödinger equation: where is the operator formed from the Hamiltonian with the replacement and . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Canonical quantum gravity」の詳細全文を読む スポンサード リンク
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