Variation principle -- looking for resources to read and understand

[Pouramat]

Summary:: Can anyone introduce an informative resource with solved examples for learning variation principle?

For example I cannot do the variation for the electromagnetic lagrangian when $A_\mu J^\mu$ added to the free lagrangian and also some other terms which are possible:
$$
L = \sqrt{-g}(\frac{-1}{4}F^{\mu \nu}F_{\mu \nu}+A_\mu J^\mu)
$$
also I want to add $L' = \beta R^{\mu \nu} g^{\rho \sigma}F_{\mu \rho}F_{\nu \sigma}$ to lagrangian and then do the variation to see what is the difference, but I cannnot.
Do you know any good resources to understand with solved examples?

 

[PeroK]

How have you got this far in your physics studies without learning the Lagrangian formulation and variational principle?

I must have at least four text-books that cover this in one form or other. E.g. Spacetime Geometry, by Sean Carroll.

 

[Pouramat]

How have you got this far in your physics studies without learning the Lagrangian formulation and variational principle?

I must have at least four text-books that cover this in one form or other. E.g. Spacetime Geometry, by Sean Carroll.

Can you give me another reference except Carroll?

 

[PeroK]

Can you give me another reference except Carroll?

Emily Noether's Wonderful Theorem - Neuenschwander

SR and Classical Field Theory (The Theoretical Minimum) - Susskind

Elementary Particles - Griffiths

QFT for the Gifted Amateur - Lancaster & Blundell

QFT in a Nutshell - Zee

 

[vanhees71]

I would first study the action principle within classical mechanics and then classical field theory before I'd go into quantum field theory. For this I'd recommend Landau and Lifshitz vols. 1 and 2.

If you start with the latter, don't take Zee's book. It's fun to read if you know the subject from somewhere else. It's not a good source to start learning it, because it wants to put too much in the nutshell and is thus too superficial to explain QFT for a beginner. Lancaster and Blundell is way better.