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Book/PDF # Field Theory / Langrangians / Variations

  1. Aug 14, 2013 #1

    I am looking for a book / paper / pdf which covers things like

    -maxwell EM field theory
    -gravitational field theory
    -variational calculus / principle of least action
    -lagrangian mechanics
    -basic scalar fields / wave equations
    -field equations out of lagrangians
    -maybe some basic quantum field theory

    -Symmetries and Noethers Theorem
    -Non-relativistic Lagrangian Fields
    -Maxwell and GR lagrange (GR + EM field equations)
    -string theory / m-theory (optional)


    -basic field theory (lecture videos)
    -calculus of variations (but almost no experience)
    -basic general relativity

    Examples of things it should contain:


    ##\delta g_{ab}##

    ##\delta \Gamma^{a}_{bc}##

    ##\mathcal{L}_G = \sqrt{-g} R##

    ##S=\frac{1}{16\,\pi}\int \mathrm{d}^4x \sqrt{-g}\left(\phi\, R - \omega\,\phi^{-1}\partial_{\mu}\phi\,\partial^{\mu}\phi\right)+S_\mathrm{M}##

    Maxwell EM:

    ##\delta F_{ab}##

    ##F_{ab} F^{ab}##

    Other fields:

    ##\partial_\mu \phi \partial^\mu \phi##

    ##\mathcal{S} = \int \, \mathrm{d}^4 x \sum_{i=1}^n \left[ \frac{1}{2} \partial_\mu \varphi_i \partial^\mu \varphi_i - \frac{1}{2}m^2 \varphi_i^2 \right]##


    -Solutions would be nice (or at least hints)
    -quite detailed
    -no graduate math textbooks please :)
    -physics background
    -some worked examples (!)

    Thank you in advance.
    Last edited: Aug 14, 2013
  2. jcsd
  3. Aug 14, 2013 #2


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  4. Aug 14, 2013 #3
    Last edited by a moderator: May 6, 2017
  5. Aug 14, 2013 #4
    Last edited by a moderator: May 6, 2017
  6. Aug 14, 2013 #5
    Thank you.

    pretty old and not really good for learning anything?
    It seems that nobody likes those books, I have never checked them out myself though.

    already have them, they are not bad.
    But I wanted to do some "basic" field theory first, QFT will come after GR one day.

    I really liked that book. Didn't understand too much of it though... :D
    That one focuses on QM/QFT too much.

    I don't know. The whole book looks like a big mess to me :|
    More like a reference than a book to learn from.

    [these are just impressions, I haven't worked trough any of them]

    My priority at the moment is : Maxwell, GR, GR + various other fields
    Last edited by a moderator: May 6, 2017
  7. Aug 14, 2013 #6


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    Nobody likes Landau and Lifshitz? That's got to be the first time I've heard that lol. Just because a book is old doesn't mean it isn't good. These books are considered some of the most elegant in physics. Classical mechanics hasn't needed an update in years upon years upon years.
  8. Aug 14, 2013 #7
  9. Aug 14, 2013 #8
    I heard:
    -highly advanced math (written for people who know A LOT OF math)
    -you need some background already to understand them

    Do not take that one too serious :)

    That is true.

    I am only talking about the 'mechanics' edition.
  10. Aug 14, 2013 #9
    That doesn't mean that nobody like them. Quite the contrary.
  11. Aug 14, 2013 #10
    Ok. Maybe I was a bit too harsh...

    From the perspective of 'self study' they are pretty bad.
    I only remember negative reviews from people saying that it's a bad idea trying to learn
    mechanics from that book.
    Somebody also said you need to be quite a genius to understand them.

    Just telling you what I know about them.
    This might not be true, so feel free to convince me that it's a good book.
  12. Aug 14, 2013 #11
    I wouldn't say so.

    L&L's Mechanics is not an intro mechanics book, but you should be fine if you know undergrad mechanics (e.g. at the level of Fowles, Analytical Mechanics).

    There's always Goldstein if you want a tome.
  13. Aug 14, 2013 #12
    Well, I guess I listened to the wrong people then...

    This https://www.physicsforums.com/showthread.php?t=666566 made me think even less of their
    mechanics book...

    Is it true that the new books are better than the old ones, didactically?
    (This is probably the reason why I want a newer book)

    I have "Electrodynamics and Classical Theory of Fields and Particles (A. O. Barut)", which is
    quite good. But no GR...
    Last edited: Aug 14, 2013
  14. Aug 14, 2013 #13
    The first 2 chapters may still be useful review for your program.

    It may be true that because I'm more familiar with GR that Zee's "Gravity" book seems much more readable to me than his QFT book.

    I mention it because of the formula for the GR action in your original post. Zee emphasizes the action more than any other book I've seen at that level. He also covers Feynman's field theoretic approach.

    You might also like the approach in Ohanian:


    This recent book may be of interest:


    There's also the little -- and, oh dear, very old -- book by Barut:


    My favorite EM book is Schwartz, Principles of Electrodynamics, but he doesn't cover variational methods at all.
    Last edited by a moderator: May 6, 2017
  15. Aug 14, 2013 #14
    That part looks really good, but I want a lot more.

    Basically a whole book filled with that sort of stuff, doing all kinds of variations/actions.

    Just edited this one in, see my last post.

    It also has solutions, nice.

    Thanks a lot.
    Last edited by a moderator: May 6, 2017
  16. Aug 14, 2013 #15
    To be honest, of the books in the series that I have, Mechanics is the only one I've used much.

    Not as a general rule.
  17. Aug 14, 2013 #16


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    So are you basically just looking for a book on classical field theory?
  18. Aug 14, 2013 #17
    if that contains GR, EM, Scalar fields, basic QFT fields. Yes, kind of.
  19. Aug 14, 2013 #18
    I also find the whole layout confusing.

    He moves a lot of stuff into the appendices in the end of the chapter,
    but there are also appendices at the end of the book.

    Some of the things from the appendices should have been covered in the main chapter.
    I really don't know why he did that...
  20. Aug 14, 2013 #19
    Last edited by a moderator: May 6, 2017
  21. Aug 14, 2013 #20

    George Jones

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    By "basic QFT fields", do you mean basic quantum theory of free scalar fields? Free EM fields? Interacting fields, including regularization and renormalization?
  22. Aug 14, 2013 #21
    scalar fields, dirac, klein gordon, qed without 'regularization and renormalization'.

    Mostly lagrangians and field equations.

    'how to construct langrangians' (symmetries, invariance, ...) would be also interesting.
  23. Aug 14, 2013 #22

    George Jones

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    Last edited by a moderator: May 6, 2017
  24. Aug 14, 2013 #23
    Last edited by a moderator: May 6, 2017
  25. Aug 14, 2013 #24
    Your question is almost perfectly answered (bar string theory) in a mixing of Gelfand's Calculus of Variations book along with Landau volume 2, & you could use Kiselev-Krasnov's Problems & Exercises in the Calculus of Variations for exercises with answers to go along with Gelfand. The combination of these three is hours & hours & hours of poetry, the only better thing than this would be a problem book to go along with Landau in detail (hint hint :approve:), and this guy


    gives great intuition for most of volume 2! Landau is quite literally the best thing I've ever read & will continue to read for the next two years, at least...
  26. Aug 14, 2013 #25


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    Speaking of which, Padmanabhan's GR text is also something you can look into. The entirety of chapter 2 is devoted to classical fields, mainly the EM field. Later chapters include the Hamiltonian formulation of GR, which imo is more complicated than the Lagrangian formulation.
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