anonanon 152k1212 gold badges233233 silver badges398398 bronze badges $endgroup$ four $begingroup$ Which is fantastic many thanks a bunch! I also posted a similar query listed here: math.stackexchange.com/issues/2135276/… that You could have some Perception on? $endgroup$
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ε i j k ε l m n =
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Levi-Civita Attributes in 4 dimensions are carefully connected to Einstein's concept of normal relativity, which describes the curvature of spacetime within the existence of significant objects.
From this conduct, we can easily deduce what $epsilon^ ij4k $ could well be devoid of experiencing the computations once again: it is simply the result of exchanging the final two indices of $epsilon^ ijk4 $,
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The Levi-Civita tensor is Utilized in the Einstein subject equations to specific the curvature of spacetime concerning the Electrical power and momentum of matter and radiation.
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These consist of additional comprehending the geometric and physical implications of such Attributes, together with their attainable generalizations to increased dimensions along with other mathematical structures.
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E α β γ δ E ρ σ μ ν = − g α ζ g β η g γ θ g δ ι δ ρ σ μ ν ζ η θ ι E α β γ δ E ρ σ μ ν = − g α ζ g β η g γ θ g δ ι δ ζ η θ ι ρ σ μ ν E α β γ δ E α β γ δ = − 24 E α β γ δ E ρ β γ δ = − six δ ρ α E α β γ δ E ρ σ γ δ = − two δ ρ σ α β E α β γ δ E ρ σ θ δ = − δ ρ σ θ α β γ . displaystyle begin aligned E_ alpha beta gamma delta E_ rho sigma mu nu &=-g_ alpha zeta g_ beta eta g_ gamma theta g_ delta iota delta _ rho sigma mu nu ^ zeta eta theta iota E^ alpha beta gamma delta E^ rho sigma mu nu &=-g^ alpha zeta g^ beta eta g^ gamma theta g^ delta iota delta _ zeta eta theta iota ^ rho sigma mu nu E^ alpha beta gamma delta E_ alpha beta gamma delta &=-24E^ alpha beta gamma delta E_ rho beta gamma delta &=-6delta _ rho ^ alpha E^ alpha beta gamma delta E_ rho sigma gamma delta &=-twodelta _ rho sigma ^ alpha beta E^ alpha beta gamma delta E_ rho sigma theta delta &=-delta _ rho sigma theta ^ alpha beta gamma ,.finish aligned
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Do the thing is how this can affect the worth of $epsilon^ alphabetagammadelta epsilon_ alpha'beta'gamma'delta' $? $endgroup$