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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Canonical quantum gravity ： ウィキペディア英語版 Canonical quantum gravity 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, $\backslash \; =\; \backslash delta\_$ where the Poisson bracket is given by :$\backslash \; =\; \backslash sum\_^\; \backslash left($ \frac_i = \, $\backslash dot\_i\; =\; \backslash$. These equations describe a ``flow" or orbit in phase space generated by the Hamiltonian $H$. Given any phase space function $F\; (q,p)$, we have $F\; (q\_i,p\_i)\; =\; \backslash .$ 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: $(,\; \backslash hat)\; =\; i\; \backslash hbar.$ In the so-called position representation this commutation relation is realized by the choice: $\backslash hat\; \backslash psi\; (q)\; =\; q\; \backslash psi\; (q)$ and $\backslash hat\; \backslash psi\; (q)\; =\; -i\; \backslash hbar\; \backslash psi\; (q)$ The dynamics are described by Schrödinger equation: $i\; \backslash hbar\; \backslash psi\; =\; \backslash hat\; \backslash psi$ where $\backslash hat$ is the operator formed from the Hamiltonian $H\; (q,p)$ with the replacement $q\; \backslash mapsto\; q$ and $p\; \backslash mapsto\; -i\; \backslash hbar$. 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 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.