Is the Assumption for Equation 6.27 in Srednicki's QFT Implied?

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The discussion centers on the derivation of equation 6.27 from Srednicki's QFT textbook. Initially, there was confusion regarding the right-hand side (RHS) of the equation and whether an assumption about the variables was necessary. After reevaluating the Gaussian integral, the user realized their mistake in the calculations and confirmed that the equation can be derived without additional assumptions. The clarification indicates that the RHS can be reached through careful manipulation of the terms involved. Ultimately, the user concluded that their earlier concerns were unfounded.
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Homework Statement


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 e^{-(q_2-q_1)^2/(2c)} e^{-(q_1-q_0)^2/(2c)}
then I get:
-[(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}

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

Is it written in the book?



Homework Equations





The Attempt at a Solution

 
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I got the answer in (6.27) without any extra assumptions.

Do your Gaussian integral more carefully! :cool:
 
OK, I can see my mistake, it shouild be:

-[(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

So all is OK.
:-D foolish me.
 
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