Hi. I'm reading "Quantum Field Theory - Mandl and Shaw" about how to derive the cross-section and in the derivation the authors make the following argument(adsbygoogle = window.adsbygoogle || []).push({});

"For large values of T and V, we can then take

[tex] \delta_{TV}(\sum p_f' - \sum p_i) = (2\pi)^4 \delta^{(4)}(\sum p'_f - \sum p_i)[/tex]

and

[tex](**) (\delta_{TV}(\sum p_f' - \sum p_i))^2 = TV(2\pi)^4 \delta^{(4)}(\sum p'_f - \sum p_i)[/tex]"

where they earlier have defined

[tex] (2\pi)^4 \delta^{(4)}(\sum p'_f - \sum p_i) = \lim_{T,V \to \infty} \delta_{TV}(\sum p_f' - \sum p_i) = \lim_{T,V \to \infty} \int_{-T/2}^{T/2}dt\int_V d^3x \exp ( i x( \sum p_f' - \sum p_i)).[/tex]

My question is how they get in a TV factor when they take the square of that finite delta function in equation (**)? The argument is found in full detail in

http://books.google.no/books?id=Ef4...no&source=gbs_toc_r&cad=4#v=onepage&q&f=false

at page 129. And the equation that I'm wondering about it (8.5).

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# Square of a finite deltafunction

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