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

• I
• StenEdeback
In summary, the Lagrangian of a classical (non-quantum), real, scalar, relativistic field is derived from symmetry principles. It can be found using a book by Goldstein or Greiner.

#### 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

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?"

#### Attachments

• Lagrangian density classical relativistic field.jpg
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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.

StenEdeback said:
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?

StenEdeback, malawi_glenn and vanhees71
You can use symmetry principles to restrict your lagrangian

StenEdeback and vanhees71
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!

vanhees71
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 and vanhees71
Thank you! I will have plenty to read. :)

vanhees71

## 1. What is the best book for learning about Lagrangian of classical, scalar, relativistic field?

There are several books that can provide a comprehensive understanding of Lagrangian of classical, scalar, relativistic field. Some popular options include "Classical Field Theory" by Davison E. Soper, "The Variational Principles of Mechanics" by Cornelius Lanczos, and "Theoretical Physics" by Joos, Born, and Heisenberg.

## 2. What are the key concepts to understand in Lagrangian of classical, scalar, relativistic field?

Some key concepts to understand in Lagrangian of classical, scalar, relativistic field include the Lagrangian density, Euler-Lagrange equations, and the action principle. It is also important to have a strong understanding of classical mechanics and special relativity.

## 3. How does Lagrangian of classical, scalar, relativistic field differ from Lagrangian mechanics?

Lagrangian of classical, scalar, relativistic field is an extension of Lagrangian mechanics, which deals with systems of particles. Lagrangian of classical, scalar, relativistic field deals with fields, which are continuous functions in space and time.

## 4. Are there any real-world applications of Lagrangian of classical, scalar, relativistic field?

Yes, Lagrangian of classical, scalar, relativistic field has many applications in theoretical physics, specifically in the study of fundamental particles and their interactions. It is also used in the development of quantum field theories and in the study of cosmology.

## 5. Is Lagrangian of classical, scalar, relativistic field difficult to learn?

The level of difficulty in learning Lagrangian of classical, scalar, relativistic field may vary depending on an individual's background in mathematics and physics. While it may be challenging, with dedication and a strong foundation in classical mechanics and special relativity, it can be understood and applied effectively.