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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 Gauge theory gravity ： ウィキペディア英語版 Gauge theory gravity Gauge theory gravity (GTG) is a theory of gravitation cast in the mathematical language of geometric algebra. To those familiar with general relativity, it is highly reminiscent of the tetrad formalism although there are significant conceptual differences. Most notably, the background in GTG is flat, Minkowski spacetime. The equivalence principle is not assumed, but instead follows from the fact that the gauge covariant derivative is minimally coupled. As in general relativity, equations structurally identical to the Einstein field equations are derivable from a variational principle. A spin tensor can also be supported in a manner similar to Einstein–Cartan–Sciama–Kibble theory. GTG was first proposed by Lasenby, Doran, and Gull in 1998 as a fulfillment of partial results presented in 1993. The theory has not been widely adopted by the rest of the physics community, who have mostly opted for differential geometry approaches like that of the related gauge gravitation theory. ==Mathematical foundation== The foundation of GTG comes from two principles. First, ''position-gauge invariance'' demands that arbitrary local displacements of fields not affect the physical content of the field equations. Second, ''rotation-gauge invariance'' demands that arbitrary local rotations of fields not affect the physical content of the field equations. These principles lead to the introduction of a new pair of linear functions, the position-gauge field and the rotation-gauge field. A displacement by some arbitrary function ''f'' :$x\; \backslash mapsto\; x\text{'}=f(x)$ gives rise to the position-gauge field defined by the mapping on its adjoint, :$\backslash bar\}\text{'}(a,x)=\backslash bar(a),f(x)),$ which is linear in its first argument and ''a'' is a constant vector. Similarly, a rotation by some arbitrary rotor ''R'' gives rise to the rotation-gauge field :$\backslash bar\}\text{'}(a,x)=R\backslash bar-2a\backslash cdot\backslash nabla\; RR^.$ We can define two different covariant directional derivatives :$a\; \backslash cdot\; D\; =\; a\; \backslash cdot\; \backslash bar\backslash mathsf(\backslash mathsf(a))$ :$a\; \backslash cdot\; \backslash mathcal\; =\; a\; \backslash cdot\; \backslash bar(\backslash mathsf(a))$ or with the specification of a coordinate system :$D\_\; =\; \backslash partial\_+\backslash frac\backslash Omega\_$ :$\backslash mathcal\_\; =\; \backslash partial\_+\backslash Omega\_\; \backslash times\; ,$ where × denotes the commutator product. The first of these derivatives is better suited for dealing directly with spinors whereas the second is better suited for observables. The GTG analog of the Riemann tensor is built from the commutation rules of these derivatives. :$()\backslash psi=\backslash frac\backslash mathsf\_\backslash psi$ :$\backslash mathcal(a\; \backslash wedge\; b)=\backslash mathsf(\backslash mathsf(a\; \backslash wedge\; b))$ 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「Gauge theory 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.