任意复双向量的不可约双线性张量伴随
Irreducible bilinear tensorial concomitants of an arbitrary complex bivector
摘要：
在四维时空中导出了任意复反对称价2张量的不可约双线性张量伴随。此外，这些双线性伴随是对称（或反对称），自对偶（或反自对偶），和埃尔米特形式的反对称张量。反对称二价张量或双向量的一个重要例子是电磁场强度张量，它通常被视为实值。在推广到复值双向量时，作者发现了著名的电磁标量不变量和应力-能量-动量张量的厄米形式，但也发现了几个新的总价2和4张量。这些张量与黎曼张量、外尔张量和里奇张量在代数上有相似之处。
英文摘要：
Irreducible bilinear tensorial concomitants of an arbitrary complex antisymmetric valence-2 tensor are derived in four-dimensional spacetime. In addition these bilinear concomitants are symmetric (or antisymmetric), self-dual (or anti-self-dual), and hermitian forms in the antisymmetric tensor. An important example of an antisymmetric valence-2 tensor, or bivector, is the electromagnetic field strength tensor which ordinarily is taken to be real-valued. In generalizing to complex-valued bivectors, the authors find the hermitian form versions of the well-known electromagnetic scalar invariants and stress-energy-momentum tensor, but also discover several novel tensors of total valence 2 and 4. These tensors have algebraic similarities to the Riemann, Weyl, and Ricci tensors.
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