Learn the Art of Indexology to Writing Lagrangians with Tensors

[taishizhiqiu]

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?

 

[DEvens]

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]

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.

A book on topological insulator:
https://books.google.com.hk/books?i...w4L#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

 

[DEvens]

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.

 

[taishizhiqiu]

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.

 

[DEvens]

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/