Dimensionally dependent tensor identities by double antisymmetrization
Dimensionally dependent tensor identities by double antisymmetrization
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双反对称的维度相关张量恒等式
DOI：
10.1063/1.1425428
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发表时间：
2001
影响因子：
1.3
通讯作者：
A. Hoglund
中科院分区：
文献类型：
--
作者：
S. Edgar;A. Hoglund
几年前，洛夫洛克证明了一些显然不相关的张量恒等式有一个共同的结构，并且都可以被认为是n维空间中一对涉及无迹（p，p）-形式的基本恒等式的推论，其中2 p <$n。我们推广了Lovelock的结果，并利用与n维空间中的任何张量相关联的一个基本张量恒等式是通过在n+1个指标上反对称化而得到的这一事实，我们为所有无迹（k，l）-形式建立了一个非常一般的“主”恒等式。然后，我们将展示如何其他各种特殊的身份是直接和简单的后果，这个主身份，特别是我们直接应用到麦克斯韦，Lanczos，Ricci，贝尔，和贝尔-罗宾逊张量，并演示如何标量之间的关系不变量的黎曼张量可以在一个系统的方式进行调查。
Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p⩾n. We generalize Lovelock’s results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrizing over n+1 indices, we establish a very general “master” identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel, and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.