Best book for Lagrangian of classical, scalar, relativistic field?

[StenEdeback]

Hi all experts!

I would like to read about the Lagrangian of a classical (non-quantum), real, scalar, relativistic field and how it is derived. What is the best book for that purpose?

Best regards,
Sten Edebäck

 

[Orodruin]

What aspects that were not covered by your latest thread do you want to know about? There really is not much more to it.

 

[StenEdeback]

Well, I am still curious about the formula in the attached file. It is not the same as the Lagrangian that I am used to. My question is really: "How do you arrive at the Lagrangian formula in the attached file? And how do you prove that it is useful, that is describes a physical system?"

 

[Orodruin]

Generally, you do not arrive at a Lagrangian. You assume a Lagrangian and from that you compute the equations of motion and compare to experiments. In some cases, it is possible to make educated guesses regarding what the Lagrangian should be based on what you know about a system.

It is not the same as the Lagrangian that I am used to.

It seems to be the standard Lagrangian for a scalar field. What Lagrangian are you used to?

 

[malawi_glenn]

You can use symmetry principles to restrict your lagrangian

 

[StenEdeback]

Thank you! I have understood now that you make an "educated guess" to find the Lagrangian and then check if it works. My problem is basically that I need knowledge of classical relativistic fields, so I have now started to read the book "Special relativity and classical field theory" by Leonard Susskind and Art Friedman, and that has already spread some light over my foggy thoughts. So, to study Quantum Field Theory I first need to study some Classical Field Theory. It is the same situation as when I started to study String Theory which I was curious about. After a while I found that I needed knowledge about Quantum Field Theory. So I started reading at the top and then needed to go down stepwise. It is still very interesting and fun. And Physics Forums have knowledgeable and helpful people, which is very valuable to me. Thank you so much again!

 

[malawi_glenn]

Chapter 13 in Goldstein's classical mechanics is a decent read.

And then you realize that in order to study this chapter, you need to read many more chapters in that book.
And so on :)

Chapter 2 in Greiners "Field quantization"

Chapter 1 - Tongs qft lecture notes https://www.damtp.cam.ac.uk/user/tong/qft.html

 

[StenEdeback]

Thank you! I will have plenty to read. :)