Learning indexology for writing Lagrangians with tensors

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taishizhiqiu
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I recently read that indexology is the art of writing a Lagrangian by just knowing how many dimensions it has and how to contract tensors. I am very interested in this technique, but I cannot find any reference. Can anyone give me a guidance or a reference?
 
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Um... You read this where? You might get a scalar from this. But a Lagrangian has to satisfy a few more conditions than just being a scalar.
 
taishizhiqiu said:
A book on topological insulator:
https://books.google.com.hk/books?id=_7r_UqFN0IEC&pg=PA164&lpg=PA164&dq=indexology+lagrangian&source=bl&ots=w58F45Dt84&sig=mdnXxwIquWEnYnGXkkQcZbWxAW0&hl=en&sa=X&ved=0CCIQ6AEwAWoVChMIx7G6jtiexwIVljKICh1c9w4L#v=onepage&q=indexology lagrangian&f=false

and I found a pdf:
https://web2.ph.utexas.edu/~gleeson/RelativityNotesAppendixC.pdf

but I don't think it will help much

Actually, the first one does help. It talks about the other conditions a Lagrangian must satisfy for an electromagnetic field. That is, you need more than just the dimension and how to contract tensors.
 
DEvens said:
Actually, the first one does help. It talks about the other conditions a Lagrangian must satisfy for an electromagnetic field. That is, you need more than just the dimension and how to contract tensors.
Oh, I think I didn't express myself clearly.

The first book is where I first read about indexology and that's why I asked such a question.

I basically understand the technique. What I want to know is more details. For example, I don't know why only ##\delta_{\alpha\beta}## and ##\epsilon_{\mu\nu\lambda}## is the only two isotropic tensors and I don't even know what are isotropic tensors. That's why I am here asking for reference.
 
taishizhiqiu said:
I basically understand the technique. What I want to know is more details. For example, I don't know why only ##\delta_{\alpha\beta}## and ##\epsilon_{\mu\nu\lambda}## is the only two isotropic tensors and I don't even know what are isotropic tensors. That's why I am here asking for reference.

Google is your friend.

http://mathworld.wolfram.com/IsotropicTensor.html
http://www.damtp.cam.ac.uk/user/reh10/lectures/nst-mmii-chapter3.pdf
http://www2.ph.ed.ac.uk/~rhorsley/SI12-13_socm/lec08.pdf
https://www.physicsforums.com/threads/isotropic-tensors.106292/