2005/09/11 by T. D. Carozzi, J. Bergman, Carozzi, T. D. +2 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Aerospace Engineering and Control Systems #Matrix Theory and Algorithms #Vehicle Dynamics and Control Systems #math-ph #math.MP #msc:15A72 #msc:78A25 #msc:83A05
paper · pdf · doi:10.48550/arxiv.math-ph/0509019
9 pages, 0 figures, submitted to J. Math. Phys
arxiv created 2005/09/11 · arxiv updated 2009/12/01
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.