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RexcirusRexcirus 43544 silver badges1515 bronze badges $endgroup$ 2 $begingroup$ Your ultimate expression would not make much feeling: The LHS has totally free indices $i,j,k$ whereas your RHS has free indices $i,j,l$. $endgroup$
or Minkowski Place. The values of your Levi-Civita symbol are independent of any metric tensor and coordinate method. Also, the precise term "symbol" emphasizes that it is not a tensor due to the way it transforms amongst coordinate techniques; nonetheless it can be interpreted to be a tensor density.
These properties are important for comprehending the habits from the tensor in various coordinate techniques.
From this habits, we can certainly deduce what $epsilon^ ij4k $ will be with out dealing with the computations Again: it is simply the result of exchanging the final two indices of $epsilon^ ijk4 $,
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This tensor should not be perplexed With all the tensor density industry talked about earlier mentioned. The presentation On this portion closely follows Carroll 2004.
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Using the capital pi notation Π for regular multiplication of figures, an specific expression for that symbol is:[citation required]
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Which can be the denominator from the Brier rating for joint a number of variables predictions? a lot more sizzling concerns
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Do you see how this may impact the value of $epsilon^ alphabetagammadelta epsilon_ alpha'beta'gamma'delta' $? $endgroup$