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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 gravitation theory ： ウィキペディア英語版 gauge gravitation theory In quantum field theory, gauge gravitation theory is the effort to extend Yang–Mills theory, which provides a universal description of the fundamental interactions, to describe gravity. It should not be confused with the related but distinct gauge theory gravity. The first gauge model of gravity was suggested by R. Utiyama in 1956〔R Utiyama, Invariant theoretical interpretation of interaction, Physical Review 101 (1956) 1597. 〕 just two years after birth of the gauge theory itself. However, the initial attempts to construct the gauge theory of gravity by analogy with the gauge models of internal symmetries encountered a problem of treating general covariant transformations and establishing the gauge status of a pseudo-Riemannian metric (a tetrad field). In order to overcome this drawback, representing tetrad fields as gauge fields of the translation group was attempted.〔F.Hehl, J. McCrea, E. Mielke, Y. Ne'eman, Metric-affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilaton invariance, Physics Reports 258 (1995) 1. 〕 Infinitesimal generators of general covariant transformations were considered as those of the translation gauge group, and a tetrad (coframe) field was identified with the translation part of an affine connection on a world manifold $X$. Any such connection is a sum $K=\backslash Gamma\; +\; \backslash Theta$ of a linear world connection $\backslash Gamma$ and a soldering form $\backslash Theta=\; \backslash Theta\_\backslash mu^a\; dx^\backslash mu\backslash otimes\backslash vartheta\_a$ where $\backslash vartheta\_a=\backslash vartheta\_a^\backslash lambda\backslash partial\_\backslash lambda$ is a non-holonomic frame. For instance, if $K$ is the Cartan connection, then $\backslash Theta=\backslash theta=dx^\backslash mu\backslash otimes\backslash partial\_\backslash mu$ is the canonical soldering form on $X$. There are different physical interpretations of the translation part $\backslash Theta$ of affine connections. In gauge theory of dislocations, a field $\backslash Theta$ describes a distortion.〔C.Malyshev, The dislocation stress functions from the double curl $T(3)$-gauge equations: Linearity and look beyond, Annals of Physics 286 (2000) 249. 〕 At the same time, given a linear frame $\backslash vartheta\_a$, the decomposition $\backslash theta=\backslash vartheta^a\backslash otimes\backslash vartheta\_a$ motivates many authors to treat a coframe $\backslash vartheta^a$ as a translation gauge field.〔M. Blagojević, Gravitation and Gauge Symmetries (IOP Publishing, Bristol, 2002).〕 Difficulties of constructing gauge gravitation theory by analogy with the Yang-Mills one result from the gauge transformations in these theories belonging to different classes. In the case of internal symmetries, the gauge transformations are just vertical automorphisms of a principal bundle $P\backslash to\; X$ leaving its base $X$ fixed. On the other hand, gravitation theory is built on the principal bundle $FX$ of the tangent frames to $X$. It belongs to the category of natural bundles $T\backslash to\; X$ for which diffeomorphisms of the base $X$ canonically give rise to automorphisms of $T$.〔I. Kolář, P. W. Michor, J. Slovák, Natural Operations in Differential Geometry (Springer-Verlag, Berlin, Heidelberg, 1993).〕 These automorphisms are called general covariant transformations. General covariant transformations are sufficient in order to restate Einstein's General Relativity and metric-affine gravitation theory as the gauge ones. In terms of gauge theory on natural bundles, gauge fields are linear connections on a world manifold $X$, defined as principal connections on the linear frame bundle $FX$, and a metric (tetrad) gravitational field plays the role of a Higgs field responsible for spontaneous symmetry breaking of general covariant transformations.〔D.Ivanenko, G.Sardanashvily, The gauge treatment of gravity, Physics Reports 94 (1983) 1. 〕 Spontaneous symmetry breaking is a quantum effect when the vacuum is not invariant under the transformation group. In classical gauge theory, spontaneous symmetry breaking occurs if the structure group $G$ of a principal bundle $P\backslash to\; X$ is reducible to a closed subgroup $H$, i.e., there exists a principal subbundle of $P$ with the structure group $H$.〔L. Nikolova, V. Rizov, Geometrical approach to the reduction of gauge theories with spontaneous broken symmetries, Reports on Mathematical Physics 20 (1984) 287. 〕 By virtue of the well-known theorem, there exists one-to-one correspondence between the reduced principal subbundles of $P$ with the structure group $H$ and the global sections of the quotient bundle $P/H\backslash to\; X$. These sections are treated as classical Higgs fields. The idea of the pseudo-Riemannian metric as a Higgs field appeared while constructing non-linear (induced) representations of the general linear group $GL(4,\backslash mathbb\; R)$, of which the Lorentz group is a Cartan subgroup.〔M. Leclerk, The Higgs sector of gravitational gauge theories, Annals of Physics 321 (2006) 708. 〕 The geometric equivalence principle postulating the existence of a reference frame in which Lorentz invariants are defined on the whole world manifold is the theoretical justification of that the structure group $GL(4,\backslash mathbb\; R)$ of the linear frame bundle $FX$ is reduced to the Lorentz group. Then the very definition of a pseudo-Riemannian metric on a manifold $X$ as a global section of the quotient bundle $FX/O(1,3)\backslash to\; X$ leads to its physical interpretation as a Higgs field. The physical reason for world symmetry breaking is the existence of Dirac fermion matter, whose symmetry group is the universal two-sheeted covering $SL(2,\backslash mathbb\; C)$ of the restricted Lorentz group, $SO^+(1,3)$.〔G. Sardanashvily, O.Zakharov, Gauge Gravitation Theory (World Scientific, Singapore, 1992).〕 == See also == 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 gravitation theory」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.