Jason (jcreed) wrote,

Slogged through some not-super-fun debugging at work. Decided to stay at home and nap and recharge my introvert batteries instead of trying to make it out to dinner again tonight.

I keep looking at Cvitanovic's crazy book (and if you doubt that it's crazy, look at the bottom of p118 of this) and trying to figure out where he actually proves the theorem that he so intriguingly seems to claim:

That there are essentially only two tensors that are invariant under all rotations in SO(3), the kronecker delta and the Levi-Civita ε tensor: any other (rotation-invariant) tensor is some contraction of a bunch of copies of those.

Anyone know if this is actually true, and if so, how to prove it? I think I convinced myself of it for all 2-, 3-, and 4-argument tensors, but I don't see any pattern forming, and directly reasoning in 3 x 5 = 15 dimensions scares me.
Tags: math

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