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

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Discussion Overview

The discussion centers around the search for recommended literature on the Lagrangian of a classical, real, scalar, relativistic field, including how it is derived and its applications. Participants explore various resources and methodologies related to classical field theory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks recommendations for books that cover the derivation of the Lagrangian for a classical scalar relativistic field.
  • Another participant questions what additional aspects the original poster is interested in, suggesting that the topic may be sufficiently covered in previous discussions.
  • A participant expresses confusion about a specific Lagrangian formula and asks how it can be derived and validated as useful for describing a physical system.
  • It is suggested that Lagrangians are often assumed based on educated guesses, which are then tested against experimental results.
  • Symmetry principles are mentioned as a means to restrict the form of the Lagrangian.
  • A participant shares their experience of needing foundational knowledge in classical relativistic fields before tackling Quantum Field Theory, indicating a stepwise approach to learning.
  • Recommendations for specific chapters in various texts, such as Goldstein's classical mechanics and Greiner's "Field Quantization," are provided as useful resources.

Areas of Agreement / Disagreement

Participants generally agree on the importance of foundational knowledge in classical field theory before advancing to more complex topics. However, there is no consensus on the best resources or methods for deriving the Lagrangian, and multiple viewpoints on the approach to understanding Lagrangians are presented.

Contextual Notes

Some participants express uncertainty regarding the specific Lagrangian formulas and their derivations, indicating a need for further clarification and exploration of the topic.

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

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  • Lagrangian density classical relativistic field.jpg
    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?
 
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You can use symmetry principles to restrict your lagrangian
 
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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!
 
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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
 
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Thank you! I will have plenty to read. :)
 
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