I General Form of Fourth Rank Isotropic Tensor: A Scientific Inquiry

[LuccaP4]

I have this statement:

Find the most general form of the fourth rank isotropic tensor. In order to do so:
- Perform rotations in $\pi$ around any of the axes. Note that to maintain isotropy conditions some elements must necessarily be null.
- Using rotations in $\pi / 2$ analyze the non-zero elements. Note that after discarding the shape of the tensor can be reduced to:

$T_{lmno}=\alpha\delta_{lm}\delta_{no}+\beta\delta_{ln}\delta_{mo}+\gamma\delta_{lo}\delta_{mn}+\chi\delta_{lmno}$​

$\alpha$, $\beta$, $\gamma$, $\chi$ are constants
- Using an infinitesimal rotation prove that $\chi=0$.

Can anyone recommend me some bibliography so I can solve this? I don't find this way to obtain the tensor in my textbooks.

 

[martinbn]

I think you have given way too much background information. Try to remove some and then ask your question, otherwise no one will be able to answer.