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Reading on the book "peskin schroeder an introduction to quantum field theory" the cross section for the production of pairs, it is not clear to me why in the calculation of the total cross section it is enough to integrate from {0 , Pi / 2}.

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It says so in the text; the photons are identical. If you would integrate from 0 to $\pi$ you would be double-counting as the situation with $\theta \in [\pi/2,\pi ]$ is identical to the one with $\theta \in [0,\pi/2 ]$.

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