论文标题
Doplicher-fredenhagen-Roberts非共同时空的一般相对性公式
A general relativity formulation for the Doplicher-Fredenhagen-Roberts noncommutative space-time
论文作者
论文摘要
在弯曲的时空中提出了Doplicher，Fredenhagen和Roberts（DFR）非交通（NC）形式主义。在DFR方法中，NC参数被提升为时空的坐标集。结果，在此空间上定义的场理论包含额外的维度。我们提出了一个包含新坐标的度量，以解释该扩展空间的长度测量值。我们将此扩展度量的Minkowski部分提升为弯曲的歧管中定义的度量。因此，我们可以建立具有额外维度的NC引力模型。基于弯曲度量，我们提出了爱因斯坦 - 希尔伯特（Einstein-Hilbert）的作用，以描述DFR空间上的NC重力模型。我们介绍引力场方程的NC版本。在场方程中考虑了弱场近似，以获得DFR空间上重力传播的波方程。
The Doplicher, Fredenhagen and Roberts (DFR) noncommutative (NC) formalism is propose in a curved space-time. In DFR approach, the NC parameter is promoted to the set of coordinates of the space-time. As consequence, the field theory defined on this space contains extra dimensions. We propose a metric containing the new coordinates to explain the length measurements of this extended space. We promote the Minkowski part of this extended metric to a metric defined in a curved manifold. Thus, we can build up a NC gravitation model with extra-dimensions. Based on the curved metric, we propose an Einstein-Hilbert action to describe the NC gravitation model on the DFR space. We present the NC version for the gravitational field equations. The weak field approximation is considered in the field equations to obtain the wave equations for the graviton propagation on the DFR space.
