论文标题
相对论变形运动学：从平坦到弯曲的空间
Relativistic deformed kinematics: from flat to curved spacetimes
论文作者
论文摘要
在过去的二十年中，已经研究了双重特殊的相对论，这是一种超越特殊相对论运动学的方式，试图捕获量子引力理论的残留效应。特别是，在双重特殊的相对论中，Einstenian相对性原理被普遍化，从而增加了光的速度，另一种相对论不变的Planck Energy。文献中有几篇论文显示了这种变形的运动学与弯曲的动量空间之间的联系。在这里，我们回顾了如何以严格的方式从几何成分中得出这种运动学，以及在弯曲时空时如何将它们推广。对于最后一个目标，必须考虑针对所有相位变量（即所谓的广义汉密尔顿空间）的特定几何形状。这种结构使我们能够在这些理论中定义一个时空，实际上，这取决于该动量。然后，从这种依赖势头的度量开始，我们还修改了几个广义相对论的概念，最终目的是建立一个自,，几何结构，可以从中探索量子重力现象学。
Doubly special relativity has been studied for the last twenty years as a way to go beyond the special relativistic kinematics, trying to capture residual effects of a quantum gravity theory. In particular, in doubly special relativity the Einstenian relativity principle is generalized, adding to the speed of light another relativistic invariant, the Planck energy. There are several papers in the literature showing a connection between this deformed kinematics and a curved momentum space. Here we review how such kinematics can be derived from geometrical ingredients in a rigorous way, and how they can be generalized when regarding a curved spacetime. For the last aim, it is mandatory to consider a particular geometry for all phase-space variables, the so-called generalized Hamilton spaces. This construction allows us to define a spacetime in these theories, which in fact depends on the momenta. Then, starting from such a momentum dependent metric, we also revise several concepts of general relativity, with the final aim of establishing a self-consistent geometrical structure from which quantum gravity phenomenology can be explored.
