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Srednicki 43.10

  1. Jul 1, 2011 #1
    Trivial question...

    How exactly does the minus sign arise in eq. 43.10? The sentence below states because the functional derivative goes through one spinor, but I can't see how that works...

    book is online here http://www.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf

    equation 43.10 is on pdf page 273

    thank you
     
  2. jcsd
  3. Jul 1, 2011 #2
    i'll take a shot.

    let me argue by analogy, maybe making the rule plausible. suppose i have anticommuting
    numbers x,y,h. and i'm given the expression yx and i want to differentiate it with respect to x.

    lacking any better choice i form the difference quotient
    [tex]\frac{d}{dx}(yx) = \lim_{h \rightarrow 0} \frac{1}{h} ( y(x+h) - yx ) [/tex]
    [tex] = \lim_{h \rightarrow 0} \frac{1}{h} yh [/tex]
    now because the numbers are anticommuting i can't just cancel h. i have to first swap
    yh or h^(-1) and y and then i can cancel.

    [tex] = \lim_{h \rightarrow 0}\left( -y \frac{1}{h} h \right)= -y [/tex]
     
  4. Jul 2, 2011 #3
    qbert, I thank you very much!
     
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