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Irreducible bilinear tensorial concomitants of an arbitrary complex bivector

T. D. Carozzi·J. E. S. Bergman
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Abstract

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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T. D. Carozzi, J. E. S. Bergman. 2005-09-11. Irreducible bilinear tensorial concomitants of an arbitrary complex bivector. https://arxiv.org/abs/math-ph/0509019

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