形状动力学。概论
Shape Dynamics. An Introduction
摘要：
形状动力学是一个完全背景独立的动力学理论的普遍框架，其中所有的绝对元素都被消除了。对于粒子来说，只有描述瞬时粒子构形形状的变量才是动态的。在黎曼三几何的情形中，唯一的动力学变量是决定角度的度规部分。局部比例因子不起作用。这导致了引力的形状动力学理论，其中广义相对论的四维同形不变性被三维同形不变性和三维共形不变性所取代。尽管对称群有这种差异，但值得注意的是，两种理论--形状动力学和广义相对论--的预言在由常平均外曲率超曲面构成的时空叶理上是一致的。然而，这两个理论是不同的，形状动力学有一个更严格的解决方案。有迹象表明，形状动力学的对称群使它更容易量子化，从而更容易产生量子引力。这个介绍介绍了在简单的条款的参数形状动力学，其实现技术，并调查现有的结果。
英文摘要：
Shape dynamics is a completely background-independent universal framework of dynamical theories from which all absolute elements have been eliminated. For particles, only the variables that describe the shapes of the instantaneous particle configurations are dynamical. In the case of Riemannian three-geometries, the only dynamical variables are the parts of the metric that determine angles. The local scale factor plays no role. This leads to a shape-dynamic theory of gravity in which the four-dimensional diffeomorphism invariance of general relativity is replaced by three-dimensional diffeomorphism invariance and three-dimensional conformal invariance. Despite this difference of symmetry groups, it is remarkable that the predictions of the two theories -- shape dynamics and general relativity -- agree on spacetime foliations by hypersurfaces of constant mean extrinsic curvature. However, the two theories are distinct, with shape dynamics having a much more restrictive set of solutions. There are indications that the symmetry group of shape dynamics makes it more amenable to quantization and thus to the creation of quantum gravity. This introduction presents in simple terms the arguments for shape dynamics, its implementation techniques, and a survey of existing results.
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