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There is no simple way to fix this error. The eqn (8.54) is correct and carries the minus sign. This tells me that the minus sign in eqn (8.53) is correct. The minus sign in [itex]-32(p_2P_1')(p_2'p_1)[/itex] is also correct and thus I am led to believe that the minus sign in the unnumbered eqn is incorrect. This opens a can of worms.

In passing from the first line of that unnumbered eqn to the second line, it is necessary to commute the [itex]u(p_2')[/itex] from the extreme right hand side past 7 other fermion operators to the extreme left hand side. According to Feynman rule 8 on page 120, this should cause a sign change in the second line of the eqn and fix the problem.

If rule 8 is not supposed to be applied here, then why not?

If rule 8 is supposed to be applied, then this opens up other problems. For instance, on page 136, starting with eqn (8.41a), there are various places where minus signs are needed, but missing. Basically, A and B should have them, but the product X does not need one. A worse problem shows up in eqns (8.78) on page 146. Each of the four right hand sides would require a minus sign and thus [itex]|\mathcal{M}|^2[/itex] would be negative.

A possible way out of this dilemna would be to notice that in taking the complex conjugate of [itex]\mathcal{M}_a[/itex] it is necessary to commute two fermion operators and this would provide the extra minus sign necessary to make the square of the amplitude positive.

If rule 8 is not supposed to be applied here, then why not?

If rule 8 is supposed to be applied, then this opens up other problems. On page 132, in passing from eqn (8.23) to the unnumbered eqn below it, a fermion operator must be commuted past three other fermion operators and this would introduce a minus sign. I'm not sure where things stand any more.

Can someone please straighten me out?