定向拟阵理论与（2+2）和八维圈量子引力
Oriented matroid theory and loop quantum gravity in (2+2) and eight dimensions
摘要：
我们在（2+2）（两个时间和两个空间维度）和8维空间中建立了定向拟阵理论和圈量子引力之间的联系。我们首先观察到，超对称性意味着实数，复数，四元数和八元数的结构常数可以与chirotope概念。这意味着，除其他事项外，赋范司代数，这是唯一可能的1，2，4或8维，是链接到定向拟阵理论。因此，我们认为发展8维圈量子引力的可能性是一个重要的选择。此外，我们表明，在4维，圈量子引力理论在（1+3）或（0+4）签名不是唯一的可能性。事实上，我们表明，与（2+2）-签名相关的环量子引力也可能是一个有趣的物理结构。
英文摘要：
We establish a connection between oriented matroid theory and loop quantum gravity in (2+2) (two time and two space dimensions) and 8-dimensions. We start by observing that supersymmetry implies that the structure constants of the real numbers, complex numbers, quaternions and octonions can be identified with the chirotope concept. This means, among other things, that normed divisions algebras, which are only possible in 1,2, 4 or 8-dimensions, are linked to oriented matroid theory. Therefore, we argue that the possibility for developing loop quantum gravity in 8-dimensions must be taken as important alternative. Moreover, we show that in 4-dimensions, loop quantum gravity theories in the (1+3) or (0+4) signatures are not the only possibilities. In fact, we show that loop quantum gravity associated with the (2+2)-signature may also be an interesting physical structure.
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