Invariant tensors


by Heirot
Tags: invariant, tensors
Heirot
Heirot is offline
#1
Dec22-12, 12:11 AM
P: 151
It is often stated that the Kronecker delta and the Levi-Civita epsilon are the only (irreducible) invariant tensors under the Lorentz transformation. While it is fairly easy to prove that the two tensors are indeed invariant wrt Lorentz transformation, I have not seen a proof that there aren't any more such tensors.

So, my question is, how to find all invariant tensors under some (linear) transformation? Is there a general procedure for this?

Thanks
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meldraft
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#2
Dec29-12, 08:40 AM
P: 280
If an object is a full tensor, then it should be invariant under any linear transformation, shouldn't it?
dextercioby
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#3
Dec29-12, 09:16 AM
Sci Advisor
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P: 11,866
Tensors as per definition are invariant objects, I guess the OP asked about tensor components in the canonical basis.


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