The Minkowski metric transforms under Lorentz transformations as
ηρσ=ημνΛμ ρΛν σ
I want to show that under a infinitesimal transformation Λμ ν=δμ ν+ωμ ν, that ωμν=−ωνμ.
I tried expanding myself: ηρσ=ημν(δμ ρ+ωμ ρ)(δν σ+ων σ)=(δνρ+ωνρ)(δν σ+ων σ)=δρσ+ωρ σ+ωσρ+ωνρων σ
Been a long time since I've dealt with tensors so I don't know how to proceed.
This post imported from StackExchange Physics at 2014-03-05 14:49 (UCT), posted by SE-user user82235