A book on topological insulator:DEvens said: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
Oh, I think I didn't express myself clearly.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.
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.
Indexology is a mathematical framework used in physics and engineering to write equations that describe the behavior of physical systems. It involves the use of tensors and indices to represent quantities such as forces, velocities, and accelerations.
Understanding indexology is crucial for scientists and engineers because it allows them to write complex equations in a concise and elegant way. It also helps in solving problems in fields such as mechanics, electromagnetism, and quantum mechanics.
A Lagrangian is a mathematical function that summarizes the dynamics of a physical system. It is typically written in terms of the system's coordinates and their derivatives and can be used to derive the equations of motion of the system.
Tensors are used in indexology to represent physical quantities and their relationships. In writing Lagrangians, tensors are used to describe the behavior of a system and its components, such as particles, fields, and forces.
While a basic understanding of mathematics is necessary, indexology can be learned by anyone with a strong foundation in calculus and linear algebra. With practice and patience, anyone can master the art of indexology and use it to solve complex physical problems.