- #1

wafelosek

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Let's consider the Lorentz group and the vicinity of the unit matrix. For each ##\hat{L}##

from such vicinity one can prove that there exists only one matrix ##\hat{\epsilon}## such that ##\hat{L}=exp[\hat{\epsilon}]##. If we take ##\epsilon^{μν}##, μ<ν, as the parameters on the Lorentz group in a vicinity of the unit matrix, then we can compute the corresponding Killing vectors as ##\xi ^μ_{αβ}=\frac{∂x′^μ}{∂ϵ^{αβ}}(\hat{ϵ}=0)## where ##x′^μ=L^μ_νx^ν##. Here is my problem: during the computations there is one line that I do not get, namely: ##\cfrac{∂L^{μν}}{∂ϵ^{αβ}}(\hat{ϵ}=0)=δ^μ_αδ^ν_β−δ^μ_βδ^ν_α##. The ## (\epsilon^{μν}) ## matrix is antisymmetric, so that is why we get the difference of the Kronecer delta?

Thank you in advance!

MW