anonanon 152k1212 gold badges233233 silver badges398398 bronze badges $endgroup$ 4 $begingroup$ That's ideal thanks a bunch! I also posted a similar question here: math.stackexchange.com/inquiries/2135276/… that You may have some insight on? $endgroup$
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ε i j k ε l m n =
or Minkowski Room. The values in the Levi-Civita symbol are unbiased of any metric tensor and coordinate technique. Also, the specific time period "image" emphasizes that it's not a tensor on account of the way it transforms in between coordinate techniques; nevertheless it can be interpreted for a tensor density.
These Houses are essential for being familiar with the behavior of your tensor in various coordinate methods.
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In any arbitrary curvilinear coordinate system and perhaps during the absence of a metric around the manifold, the Levi-Civita image as outlined over may be considered to be a tensor density subject in two other ways.
In Einstein notation, the duplication check here in the i index implies the sum on i. The prior is then denoted εijkεimn = δjmδkn − δjnδkm.
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where gab may be the representation with the metric in that coordinate system. We will equally consider a contravariant Levi-Civita tensor by elevating the indices with the metric as common,
Up to 3 sets of CTs per section might be paralleled per meter without the require for your meter multiplier