antisymmetric tensor


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antisymmetric tensor

[¦an·tē·si¦me·trik ′ten·sər]
(mathematics)
A tensor in which interchanging two indices of an element changes the sign of the element.
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An antisymmetric tensor can also be defined from the displacement [u.
Classical" electric and magnetic fields in the vacuum are joined to an antisymmetric tensor of 2nd rank
where the components of the third-rank material spin (chirality) tensor 3S are herein given via the second-rank antisymmetric tensor 2S as follows:
00] = 0, as for any antisymmetric tensor of the 2nd rank, after some algebra we obtain the other components of the field tensor [F.
i]) is the three-dimensional antisymmetric tensor of the space rotation observable angular velocities, which indices can be lifted/lowered by the metric observable tensor so that [D.
This was shown in [45], by using the simple observation that the only sl(2) singlet at the fourth power of [lambda] is in the sl(2) [direct sum] so(8) representation (0)(0200)--the four-index antisymmetric tensors (0)(0020) or (0)(0002) do not occur.