- #1
TimeRip496
- 254
- 5
As known, any Lorentz transformation matrix
##\Lambda##
must obey the relation
##\Lambda^μ{}_v####\Lambda^ρ{}_σ##gμρ=gvσ
. The same holds also for the inverse metric tensor
gvσ
which has the same components as the metric tensor itself (don't really understand why every tex formula starts from a new line), i.e.
##\Lambda^v{}_μ####\Lambda^ρ{}_σ##gvσ=gμρ
. Putting this all as a matrix relation, these two formulas are
ΛTgΛ=g , ΛgΛT=g
, where g is the metric tensor (and also the inverse metric tensor, as they are both the same).
I don't understand why is the lambda transpose and why the two different metric tensor suddenly become the same g. Is there something that I am missing out? And I a bit unsure of the inverse metric tensor stated above.
##\Lambda##
must obey the relation
##\Lambda^μ{}_v####\Lambda^ρ{}_σ##gμρ=gvσ
. The same holds also for the inverse metric tensor
gvσ
which has the same components as the metric tensor itself (don't really understand why every tex formula starts from a new line), i.e.
##\Lambda^v{}_μ####\Lambda^ρ{}_σ##gvσ=gμρ
. Putting this all as a matrix relation, these two formulas are
ΛTgΛ=g , ΛgΛT=g
, where g is the metric tensor (and also the inverse metric tensor, as they are both the same).
I don't understand why is the lambda transpose and why the two different metric tensor suddenly become the same g. Is there something that I am missing out? And I a bit unsure of the inverse metric tensor stated above.
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