论文标题
关于一般相对论的对称性
About the symmetry of general relativity
论文作者
论文摘要
在这项工作中，我们使用广义变形量规组来研究一般相对论的对称性（GR）。 GR以广义参考帧进行配制，该框架由（一般情况下的肛门工句）仿射框架字段表示。相对论的一般原理扩展到理论对广义参考帧之间过渡的不变性的要求，即相对于仿射框架字段的局部线性变换的组$ gl^g $。 gr被解释为翻译量规$ t^g_m $的量规理论，因此在时空差异性下是不变的。 $ gl^g $和$ t^g_m $组成的组$ s^g_m $，这是他们的半导向产品，是仿射框架（graf）中一般相对论的完整对称组。 Graf的$ gl^g $ invariance的结果是palatini方程，在没有扭转的情况下，该方程式进入了度量条件，反之亦然，即在Riemannian空间中相同实现。 GRAF的$ t^g_m $ invariance的后果是以超电势形式的爱因斯坦方程表示，即动态麦克斯韦方程（或Young-Mills方程）的形式。组$ s^g_m $的变形导致重力摩托车的重态度。 At the end we show that by limiting admissible reference frames (by $GL^g$-gauge fixing) from GRAF, in addition to Einstein gravity, one can obtain other local equivalent formulations of GR: general relativity in an orthonormal frame or teleparallel equivalent of general relativity, dilaton gravity, unimodular gravity, etc.
In this work we use generalized deformed gauge groups for investigation of symmetry of general relativity (GR). GR is formulated in generalized reference frames, which are represented by (anholonomic in general case) affine frame fields. The general principle of relativity is extended to the requirement of invariance of the theory with respect to transitions between generalized reference frames, that is, with respect to the group $GL^g$ of local linear transformations of affine frame fields. GR is interpreted as the gauge theory of the gauge group of translations $T^g_M$, and therefore is invariant under the space-time diffeomorphisms. The groups $GL^g$ and $T^g_M$ are united into group $S^g_M$, which is their semidirect product and is the complete symmetry group of the general relativity in an affine frame (GRAF). The consequence of $GL^g$-invariance of GRAF is the Palatini equation, which in the absence of torsion goes into the metricity condition, and vice versa, that is, is fulfilled identically in the Riemannian space. The consequence of the $T^g_M$-invariance of GRAF is representation of the Einstein equation in the superpotential form, that is, in the form of dynamic Maxwell equations (or Young-Mills equations). Deformation of the group $S^g_M$ leads to renormalisation of energy-momentum of the gravitation field. At the end we show that by limiting admissible reference frames (by $GL^g$-gauge fixing) from GRAF, in addition to Einstein gravity, one can obtain other local equivalent formulations of GR: general relativity in an orthonormal frame or teleparallel equivalent of general relativity, dilaton gravity, unimodular gravity, etc.
