Dimensionally dependent identities
Dimensionally dependent identities
复制标题
维度相关的恒等式
DOI：
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发表时间：
1970
影响因子：
0.8
通讯作者：
D. Lovelock
中科院分区：
文献类型：
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作者：
D. Lovelock
在广义相对论中，经常使用四维空间所特有的一些明显无关的恒等式。然而，通常提出的证明似乎没有共同的想法，而且，不清楚在什么阶段的维数限制起着重要的作用。本文给出了一种显式地证明维数依赖性的方法，从而使上述恒等式推广到n维空间。它还表明，上述身份都是一个更一般的身份有效的n = 4的特殊情况。
Abstract In the general theory of relativity a number of apparently unrelated identities peculiar to a 4-dimensional space are frequently used. However, the proofs usually presented appear to have no common ideas and, furthermore, it is not clear at what stage the dimensionality restriction plays a significant role. In this note a technique is presented which explicitly exhibits the dimensionality dependence and thereby enables the above identities to be generalized for n-dimensional spaces. It is also shown that the above identities are all special cases of a more general identity valid for n = 4.