八元数和真空稳定性
Octonions and vacuum stability
摘要：
本文讨论了一个与八元数有关的非平凡事实。根据论文gr-qc/0409095，最稳定的时空状态是由签名为1（-）&10（+）的11维空间中的实狄拉克矩阵描述的时空状态。内子空间是7维的，它的稳定性是由于高的“零”能量堆积密度时，使用的基本矢量的格子E_8的旋量自由度的一个对角基。非平凡的事实包括以下几点：具有八元数矩阵元素的狄拉克符号可以用来描述内部自由度空间的状态，当且仅当该空间对应于稳定的真空态或接近上述状态的状态。对于考虑这个问题的绝对不同和独立的方法，内部空间维度和特征的重合似乎预先确定了内部空间真空性质和装置，这能够构成统一相互作用理论的基础。
英文摘要：
The paper addresses one of nontrivial octonion related facts. According to paper gr-qc/0409095, the most stable space-time state is the one described by real Dirac matrices in 11-dimensional space of signature 1(-)&10(+). The internal subspace is 7-dimensional, and its stability is due to a high ``zero'' energy packing density when using an oblique-angled basis from fundamental vectors of lattice E_8 for the spinor degrees of freedom. The nontrivial fact consists in the following: Dirac symbols with octonion matrix elements can be used to describe states of the space of internal degrees of freedom if and only if the space corresponds either to stable vacuum states or states close to the just mentioned ones. The coincidence of the internal space dimension and signature for absolutely different and independent approaches to the consideration of this issue seems to predetermine the internal space vacuum properties and the apparatus, which is able to constitute the basis of the unified interaction theory.
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