- #1
LuccaP4
- 24
- 9
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:
- 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.
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.