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Representation of Lorentz group and spinors (in Peskin page 38)

  1. Mar 15, 2013 #1
    I am very confused by the treatment of Peskin on representations of Lorentz group and spinors.

    I am confronted with this stuff for the first time by the way.

    For now I just want to start by asking: If, as usual Lorentz transformations rotate and boost frames of reference in Minkowski space, are we considering now rotations and boosts in spin space?

    And does anybody know about some clear treatments on spinors and representations of the Lorentz group?

    Any help would be greatly appreciated!!
  2. jcsd
  3. Mar 15, 2013 #2


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    The best treatment about the Poincare group (it's the Poincare group not only the Lorentz group which is important in relativistic quantum-field theory!) can be found in

    S. Weinberg, Quantum Theory of Fields, Vol. I

    You also find a treatment in my QFT manuscript:

  4. Mar 15, 2013 #3


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    Ryder does a good job of discussing the spinor representation of the Lorentz group if I recall correctly. To answer your other question, you're still dealing with Minkowski space, but you're boosting and rotating spinors as opposed to the usual 4-vectors.
  5. Mar 15, 2013 #4
    this does not make sense.are you asking about how Lorentz transformation affects spinors.In that case,your question can be answered.
  6. Mar 15, 2013 #5


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    It's a dual view actually, you could well have one field configuration viewed by different inertial observers connected thorough a Lorentz/Poincare' transformations.
  7. Mar 16, 2013 #6
    To andrien. Yes I am asaking exactly that!
    How do Lorentz transformations affect spinors?

    And thanks to everybody for posting very helpful links! I'll go to the library today to get the books and I'll take a look at vanhees's notes (how did you know that I can speak German? :-D )!
  8. Mar 16, 2013 #7
    Well I think I do understand now what is happening (very generally) from dexterciobys post. Basically we still are in M spacetime, and we have intertial oberservers connected by LT but instead of looking at 4 vectors or tensors they are looking at spinors, am I correct?
  9. Mar 16, 2013 #8


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    I liked the treatment of this topic in Lambert's notes on SUSY very much. It also paves the way to SUSY for you ;)
  10. Mar 16, 2013 #9


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  11. Mar 16, 2013 #10
    A finite transformation can be constructed from infinitesimal ones in case of lorentz transformation.lorentz transformation of dirac spinor is
    ψ'=e(-iωμvSμv)ψ,it is the finite one constructed from infinitesimal ones.ωμv are antisymmetric and are 6 parameters representing boosts and rotations.S's are generators written in terms of pauli matrices.
  12. Mar 18, 2013 #11
    to andrien, that description I do know, it's just what Peskin writes in his book!

    I am looking for a real understanding of lorentz transformations and their representation in spinor space. And especially what it physically means and what the distinction between spinors and vectors are, etc.

    Ryder seems to be a very good introduction!

    I'm still searching in vanhees's script for the relevant paragraphs.

    at haushofer, do you mean the lecture notes by Neil Lambert?

    I am still looking into Weinbergs book, I didn't go quickly through the chapter to see if I can find answers to my questions, but there is a lot of standard stuff in it which one can find in peskin and other resources too.

    Well I'mm still working through the resources to resume, I'll post something when I find the good one (for me)!
  13. Mar 18, 2013 #12


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    Yes, I ment those lecture notes :)
  14. Mar 18, 2013 #13


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  15. Apr 17, 2013 #14
    Hello Everybody,

    Sorry for replying now!

    Van Hees notes and Ryder are good. I worked through Ryder and still working through Van Hees script right now.

    Would you recommend going through Weinberg chapter 2.2 to 2.7? I don't have much time right now, so I thought better study it later.

    Thanks for your support.
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