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Starting with QFT

  1. May 14, 2005 #1

    StatusX

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    I just finished an introduction to quantum mechanics class, and I was wondering where I could learn QFT on my own (including any more QM I might need to learn before I could start QFT). I have Griffiths book, and in class we covered the first 7 chapters (which includes all the basics, hydrogen, time-indep. perturbation, identical particles, and the variational principle), so I'm comfortable with this material and could learn the stuff in the rest of the book on my own. Where should I go after this?
     
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  3. May 14, 2005 #2

    ZapperZ

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    I would strongly suggest you wait till you have done perturbation theory and Second Quantization.

    Zz.
     
  4. May 14, 2005 #3

    dextercioby

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    What about dynamical systems with constraints...?All nonzero spin classical fields have either I-st class or second class constraints.

    It's not only QM.:wink: Classical field theory,too.

    Daniel.
     
  5. May 14, 2005 #4

    vanesch

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    Well, you should probably first become a bit more confortable with QM. I strongly suggest you read "Modern Quantum Mechanics" by J.J. Sakurai. I know that there are other people preferring other books for quantum mechanics per se, but you have to know that Sakurai wrote this book _especially_ as a preparation for QFT afterwards.

    A while ago I organized an internet course on this book, and some material from that period is still left on a website I set up for the occasion:

    http://perso.wanadoo.fr/patrick.vanesch/nrqmJJ/NRQM_main_page.html

    In fact the course fell on its face after the first part, because there was not much very active participation anymore. So I never got to the second part, that's why there is less material.

    cheers,
    Patrick.
     
  6. May 14, 2005 #5
    Hey Status,

    I'll put in my two cents as someone who has taken a basic hardcore QM class and then learned a lot more on my own over the years. By profession I'm not a physicist, so take it for what it's worth :wink: . I'd say that Feynman's Lectures on Physics, Volume III on QM, is a fantastic resource for getting a strong intuitive feel for QM, even though it's over 40 years old now. If you like Feynman's way of thinking, you could go from his Lectures to the Feynman and Hibbs text Quantum Mechanics and Integrals, which lays out the Feynman path integral formulation.

    I don't know enough about QFT to know how the FPI fits in to QFT. But I would also strongly recommend a very short paper by Dan Styer, "Nine formulations of quantum mechanics," Am J Physics 70(3), March 2002, p 288, that gives an overview of, well, you can guess from the title. (The FPI is one of the nine.) It may be that one of these various formulations is particularly better suited than the others as a foundation for QFT, I don't know. If you or anyone else knows, I'd be interested!

    David
     
  7. May 14, 2005 #6
    I would go to the bookstore and browse Zee's Quantum Field Theory in a Nutshell, and see how much of it you can handle. Zee is a fairly new book, and has a modern approach to QFT.

    Griffiths' Introduction to Elementary Particles is fairly accessible to a person who knows some QM, and covers Feynman diagrams at a very basic level. Also Halzen and Martin, which is a bit more difficult than Griffiths. Griffiths pretty much rips off Halzen and Martin, actually, but that's an issue independent of the quality of the textbook.
     
    Last edited: May 14, 2005
  8. May 14, 2005 #7

    dextercioby

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    Or you can do it another way:Read Feynman & Hibbs with their Path Integral text and then go to Bailin & Love "Introduction to Gauge Field Theory",Adam Hilger,2-nd Edition,1993. It covers pretty much everything from the SM,but u need to know path integrals and why are they useful in a quantum theory.

    Daniel.
     
  9. May 14, 2005 #8
    Steven Weinberg is all one needs.
     
  10. May 14, 2005 #9
    It'd be nice if they could republish Feynman and Hibbs. Costs $325 on Amazon, and all the copies in the Caltech library system are checked out.

    There's a relatively book by Mosel on path integration. No reviews on Amazon though.
     
  11. May 14, 2005 #10

    dextercioby

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  12. May 14, 2005 #11
    Cool - but more than half of the text appears to be in German.

    However, there's another one further down the list that is fully in English.
     
    Last edited: May 14, 2005
  13. May 14, 2005 #12

    StatusX

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    OK, thanks for all your help so far. So what exactly do I need to learn before I'll be ready for QFT, and where can I find it? dexter, you mentioned "nonzero spin classical fields": what is that, and do I need to know it?
     
    Last edited: May 14, 2005
  14. May 14, 2005 #13

    dextercioby

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    The name says it all:QFT is Quantum Field Theory.That is:the quantum theory of fields.It deals with quantized fields.So u'll have to get a grip on fields:what are they and what do they do and why do we need to quantize them...?What does quantization mean...?

    "Spin" of a field:the dimension of the irreducible representation of the restricted Lorentz group.Example:the scalar field corresponds to the (0,0) representation of the restricted Lorentz group and its operator is the unit operator acting on the linear space of this representation.

    That's classical field theory.What are fields & what do they do.

    Daniel.

    P.S.Will u be taking QFT in college,eventually,or not?
     
  15. May 14, 2005 #14
    I suppose you are implying that Status should focus more on the FPI than on some other formulation of QM, eg Heisenberg's matrix formulation or Schrodinger's wave mechanics, as prerequisite for QFT. Is this what you mean, and do others agree? At a conceptual level, how does the FPI lead to QFT?

    David
     
  16. May 14, 2005 #15

    dextercioby

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    Depends...I've been taught QFt both ways.In QCD and EW,the operatorial approach is useless,so why not do everything path integral...?After all,Wick's theorem looks a lot simpler playing with nonconnected Green functions,right?

    Anyway,i still hope the OP will not attempt to study QFT all by himself.He needs a teacher,lecture notes,explanations and just then self-study.

    My say.

    Daniel.
     
  17. May 14, 2005 #16

    StatusX

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    I'm finishing up my sophomore year now, and I'll be going on to grad school, where I presume I'll take some classes QFT. I just wanted to get started now because (a) I'm curious and interested in it and (b) I want to do research next year and I'd like to actually be useful, or at least stand out from some of the other undergrads. And by the way, I've always learned much, much better on my own out of a book than by going to class or talking to professors or other students.
     
  18. May 14, 2005 #17

    dextercioby

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    I see your point.If "research"is your goal,then mathematics should come first.U can't understand the pysics without a proper education in higher mathematics.And shouls have been clear ever since the first theoretical physics course you've ever had (if u have).

    Daniel.
     
  19. May 14, 2005 #18

    StatusX

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    OK, that's why I started this thread, because I don't know what I should be doing. What math should I learn? I've always just learned the math along with the physics as it was needed.
     
  20. May 14, 2005 #19
    Well it's not an either-or thing, of course. You should continue your formal studies AND continue your self-study. (I know you know that, but it's worth saying anyway.)

    David
     
  21. May 14, 2005 #20
    Do you have an idea what kind of research you're interested in? I suppose as a start: theoretical or experimental?

    David
     
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