I'm a bit confused by something Peskin & Schroeder say about differential cross sections. In my printing, this is on page 101 in the paragraph preceding the one that contains eq. 4.62:(adsbygoogle = window.adsbygoogle || []).push({});

"In the simplest case, where there are only two final-state particles, this leaves only two unconstrained momentum components, usually taken to be the angles [itex]\theta[/itex] and [itex]\phi[/itex] of the momentum of one of the particles. Integrating [itex]d\sigma/(d^3p_1d^3p_2)[/itex] over the four constrained momentum components then leaves us with the usual differential cross section [itex]d\sigma/d\Omega[/itex]."

The second sentence seems like a very odd thing to say. How do you integrate overconstrainedvariables? They have defined the generic differential cross [itex]d\sigma/(d^3p_1...d^3p_n)[/itex] as the quantity that, when integrated over any small region [itex]d^3p_1...d^3p_n[/itex] in final momentum space, gives the cross section for scattering into a state with momenta in that region. So, for two particles, if we specify small ranges for [itex]\theta[/itex] and [itex]\phi[/itex] for one of the final momenta then we have specified the entire region [itex]d^3p_1...d^3p_n[/itex] in final momentum space. We can't integrate over the remaining components because they've already been fixed. So what exactly do P&S mean?

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# Differential cross sections in Peskin & Schroeder

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