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Questions on chapter 95 in Srednickis QFT book, Supersymmetry

  1. Jun 20, 2009 #1


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    Hello all

    Since there seems that quite many here have followed Professor Srednickis QFT book, I want to ask a couple of question I have from his chapter on Supersymmetry.

    i) on page 617 he defines the kinetic term of the Chiral Superfields as:
    [tex]L_{\text{kin}} = \Phi^{\dagger} \exp(-2gV) \Phi[/tex]

    but he evaluates [tex] \Phi^{\dagger} \Phi[/tex] in eq. 95.63

    But why? the relation is not [tex] \exp(-2gV) \Phi^{\dagger} \Phi[/tex]

    Can one pull that exponential like this, even though it contains anticommuting numbers (95.62)

    ii) On page 618, he says that "From eq 95.24, we see that [tex]D^*_{\dot{a}} = - \partial ^*_{\dot{a}} [/tex] acts on a function of y, theta and theta^*

    Has anyone confirmed this? I am lost, and what is the significance of this?

    iii) How does he starts off with equation 95.68, and why is there a factor of 2, comparing with 95.16??

    If anyone has any questions on this chapter, maybe we can start a study circle and solve the problems and derivations together?

  2. jcsd
  3. Jun 20, 2009 #2


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    Yes, because V and Phi are commuting; every term in them contains an even number of Grassmann variables. I believe he writes it that way because then it generalizes to the nonabelian case, where V is a matrix.

    As for your other questions, I don't have the book handy at the moment, will try to check back later.
  4. Jun 20, 2009 #3

    The only field that is not commuting, Srednicki introduces on equation (95.65). You can tell because the field has a spinor index, (95.73) makes it concrete.


    This is correct. (95.24) proves two of the statements. The third is simple just use the definition (95.17).


    95.68 is true too. It's like a chain rule. The 2 comes out when you actually do the calculation of D_a on y^mu.
  5. Jun 20, 2009 #4


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    Thank you all for input, will get my hands more dirty tomorrow with this hehe
  6. Jun 20, 2009 #5
    I just looked at your second question again (ii), and it's somewhat tricky.

    The supercovariant derivatives (D_a) was initially defined with respect to the spacetime variable x, I think on the 2nd page of the chapter. But Srednicki is writing the field W_a in terms of a new variable y now. So the question becomes how does D_a operate on a function of y now? 95.24 says D_a (where D_a operates on a field with argument x), operating on y (which is a function of x), is zero. So D_a operated on y is zero. However, you can write that as [tex]-\partial^{*}_{a} [/tex] (where there is a dot on the 'a') because operated on y, this is zero. So basically Srednicki is rewriting D_a to operate on a space with a y coordinate instead of an x one.
  7. Jun 20, 2009 #6


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    [tex]D^*[/tex] on y and on [tex] \theta [/tex] gives zero , so the only action that it can have comes from its first term in 95.17, which is [tex]- \partial ^*_{\dot{a}} [/tex]. I am probably missing the point of your question.

    EDIT: Sorry, just realized that RedX had answered that question.
    Last edited: Jun 20, 2009
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