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Best book on relativistic QM and QFT

  1. Sep 25, 2017 #1
    I loved Modern Quantum Mechanics by Sakurai, where Quantum Mechanics is presented and worked out. Now I would like to proceed further, and learn about Relativistic Quantum Mechanics and Quantum Field Theory.

    I started by reading Sakurai's Advanced Quantum Mechanics, but later I found that the theory is much more than what is presented on that book. So, I did some searches on web, and I ended up with the following recommended books:

    - 3 volumes on QFT by Weinberg;
    - QFT by Peskin, Schroesder;
    - QFT by Schwartz.

    What book out of these three would be the best one? Or, for those who know Sakurai's Advanced QM, would it be better for me that those three above?

    Or, if there's still other good ones which I did not mention, please let me know.

    Thanks.
     
  2. jcsd
  3. Sep 25, 2017 #2

    king vitamin

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    I like all 3 of those textbooks. But I will say that Weinberg is better after you've gone through a different textbook, because it is not great for learning the basics or how to do calculations. He uses some non-standard notations and conventions which will likely frustrate you if you get stuck and try to look at a different textbook. With that said, there are some incredible insights in that book which are not found anywhere else - every few years I revisit it and learn something new.

    I think my favorite of the three is Peskin and Schroeder, but I'm biased because I use QFT for condensed matter/stat mech applications, and P&S do a great job at explaining these applications, with a whole chapter on critical exponents. Schwartz is similarly modern in its treatment, but the focus is very much on particle physics and the Standard Model, with some parenthetical discussion of the other applications. Both books are great for teaching you how to do computations, and when you're first learning a subject, sometimes it is good to dive in and do calculations before understanding everything. (Put more accurately, doing the calculations helps you understand the physics, so beginning with a book like Weinberg might simply leave you confused.)

    I am not familiar with Sakurai, though I've heard that it has a lucid treatment of certain issues. But QFT went through a revolution in the 1970s where many important theories were developed and understood, and where the non-pertuebative meaning of a QFT was largely elucidated. So Sakurai's book must be outdated if it hasn't changed much since 1967. But you shouldn't throw it out - the more resources you have, the better.
     
  4. Sep 26, 2017 #3

    dextercioby

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    Sakurai is outdated first because it uses the pesky x 4 =ict convention, then because it predates modern gauge theory.
     
  5. Sep 26, 2017 #4

    bhobba

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    QFT is one of those areas you build up to in stages. I would NOT start with Weinberg, Peskin and Schroeder; or Schwartz..

    My suggestion in order is:

    1. Physics from Symmetry:
    http://physicsfromsymmetry.com/
    2. Quantum Field Theory Dymystifyed:
    https://www.amazon.com/Quantum-Field-Theory-Demystified-McMahon/dp/0071543821
    3. Quantum Field Theory For The Gifted Amateur (I am about at this level now):
    https://www.amazon.com/Quantum-Field-Theory-Gifted-Amateur/dp/019969933X
    4. Student Friendly Quantum Field Theory: (This is about the same level as the above - but still would not skip it)
    https://www.amazon.com/Student-Friendly-Quantum-Field-Theory/dp/0984513957
    5 Quantum Field Theory In a Nutshell (have read it but would not say I understand it to the level of the above two books - its a bit terse in places for me personally. However would not attempt going further until I am fully comfortable with it)
    https://www.amazon.com/Quantum-Field-Theory-Nutshell-nutshell/dp/0691140340

    I know it's a long list, but take the word of someone who has done this himself - you will not be sorry. Things will be so much clearer when you do tackle those tomes you mentioned at the start. Of the three I prefer Weinberg - but only because I think it is the most complete and you will have a good background after those 5 books. BTW I have all those books and do not consider I am at the stage to tackle Weinberg - even though I have his three volume set.

    Thanks
    Bill
     
  6. Sep 26, 2017 #5

    bhobba

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    While I do not feel comfortable to study Weinberg yet, I of course have skimmed through it and from what little I did glean I think that is pretty accurate. It really gives fantastic insight if you are ready for it - at least that's the impression I got.

    Thanks
    Bill
     
  7. Sep 26, 2017 #6
    I appreciate very much your opinions. Thanks

    To bhobba, I will try to follow the list you have presented. I believe there are some of them available in the uni library.
     
  8. Sep 26, 2017 #7

    king vitamin

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    It's certainly accurate! And on a lot of topics it offers unique insight that really cannot be found anywhere else. But it is one of the last books I go to if I need help computing diagrams. His decision to use a non-Lorentz invariant normalization on the states results in factors showing up everywhere which disagree with every other QFT textbook I own. In my opinion, there are enough technical difficulties with doing loop diagrams to need to worry about these extra factors.

    I've been doing diagrams for long enough that it doesn't matter much, and I probably revisit Weinberg as much as the rest. But in my first couple years of learning QFT, it was not as helpful as P&S, Srednicki, Zee, and Schwartz (whose course I took before he published his book).
     
  9. Sep 26, 2017 #8
    I'd like to jump in and say that I found Student-Friendly QFT to be relatively accessible, with the material developed slowly and progressively, and explained clearly at a beginner level. It also gave me a whole new respect for the pioneers in the field, because there are some derivations that look like an explosion in the algebra factory. The thought of plowing through that work, not knowing what direction to take initially or whether you're going to hit a brick wall, is certainly daunting. The author freely admits that he holds some non-mainstream views on vacuum energy and normal ordering, but he basically mentions it in passing and goes on to present an orthodox development of QFT. I did try the Srednicki book (mostly because it was free), but found it moved way too fast for me.
    I am still really intrigued by Physics From Symmetry, but was put off by the report that there were numerous errors in the text. I have a hard enough time going through this material without trying to figure out whether there is a typo, or I'm just not following what's going on. I hope this might be corrected (or mitigated) in the future.
     
  10. Sep 26, 2017 #9
    Physics From Symmetry seems interesting mainly because it seems to derive all fundamental equations of QM and QFT from the principle of Lorentz invariance. Maybe @bhobba tell us what is his opinion with respect to the typos, i.e. whether that affects too much the reading/comprehension of the text.
     
    Last edited: Sep 26, 2017
  11. Sep 26, 2017 #10

    vanhees71

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    First of all, don't waste time with any book on "relativistic QM", i.e., relativistic QT without using QFT.

    I'd rate Schwartz, QFT and the Standard Model and the 3 vols. by Weinberg as equally good, but Schwartz is better as an introduction, while Weinberg is very comprehensive and complete, but maybe too detailed as an introduction.

    Peskin&Schroeder is also not bad in principle, but has a bit too many unfortunate typos and sometimes even conceptional weaknesses (like dimensionful arguments of logarithms even in the chapter on the renormalization group, which is kind of ironic!).
     
  12. Sep 26, 2017 #11

    vanhees71

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    Well Schwichtenberg had not too positive reviews (e.g., in Physik Journal). I've only glanced at it, and it seems indeed a bit superficial although the subject is of course very interesting and useful.

    For group-theoretical methods in physics, particularly special relativity (including a very good treatment of Wigner's famous work on the unitary irreps of the Poincare group), I like Sexl, Urbandtke, Relativity, Groups, Particles.
     
  13. Sep 26, 2017 #12

    bhobba

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    I have a copy and like it very much. I don't mind the mistakes etc - its fun picking them up.

    It is superficial (in the sense if you have seen this stuff before - but crucial if its your first exposure - it wasn't my first exposure by a long shot so I went through it pretty quick - but if it is your first exposure it will take a bit of time for it to sink in), which is why I have it as the first part of a long list of reading before Weinberg. You must build up to it and that superficiality is fine at the start. It also prepares your mind for the symmetry that is very much a part of QFT - especially Weinberg.

    I consider it an essential part of the sequence I suggested.

    Thanks
    Bill
     
    Last edited: Sep 26, 2017
  14. Sep 27, 2017 #13
    Another book you may want to look into is Robin Ticciati's "Quantum Field Theory for Mathematicians". Ticciati was a student of Sidney Coleman, and took the latter's famous course on QFT, whose influence is evident throughout the book. He develops the subject in a very clear yet rigorous manner, and despite the book's title, I would say it's accessible to anyone who has mastered the standard graduate-level physics curriculum.
     
  15. Oct 1, 2017 #14

    haushofer

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    I'd recommend "QFT for the gifted amateur" from the 10 or so QFT-books I have here.
     
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