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Chapter 6 of Srednicki's problems.

  1. Jul 9, 2014 #1

    MathematicalPhysicist

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    1. The problem statement, all variables and given/known data
    I am reading the solutions manual of Srednicki's textbook in QFT (alongside reading the textbook itself).
    Here it is:
    http://www.scribd.com/doc/87916496/Srednicki-Ms-Qft-Solutions-Rev

    So the equation that he arrives at (6.27).

    I am not sure I understand how did he arrive at the RHS?

    I mean if I write the exponent down, i.e [tex] e^{-(q_2-q_1)^2/(2c)} e^{-(q_1-q_0)^2/(2c)}[/tex]
    then I get:
    [tex]-[(q_2-q_1)^2/2c + (q_1 -q_0)^2/2c] = -[\frac{(q_2-q_0)^2}{4c} +\frac{2q_1^2-2q_1(q_2+q_0)+q_2q_0}{2c}[/tex]

    Now to get the RHS we need to assume that: [tex]q_2q_0 - 2q_1(q_2+q_0)=0[/tex] which I don't see it written in the textbook, perhaps I skipped over it...

    Is it written in the book?



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 9, 2014 #2
    I got the answer in (6.27) without any extra assumptions.

    Do your Gaussian integral more carefully! :cool:
     
  4. Jul 10, 2014 #3

    MathematicalPhysicist

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    OK, I can see my mistake, it shouild be:

    [tex] -[(q_2-q_1)^2/2x +(q_1-q_0)^2/2c] = -(q_2-q_0)^2/4c - (q_1 - (q_0+q_2)/2)^2/c [/tex]

    So all is OK.
    :-D foolish me.
     
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