Relation between particle and antiparticle matrix elements

Relation between particle and antiparticle matrix elements Because the antiparticle spinors v are related to the particle spinors u by 

But this is a number, not a matrix, and hence equal to its transpose. Thus we can write 

Comparing (1.3.11) with (1.3.9) we see that rA B(P P ) is obtained from rA B(PtP ) simply by changing the sign of the axial-vector coupling. Since we inevitably deal with the modulus squared of matrix elements, this implies simply changing the sign of the vector-axial-vector interference term in the expression for physical observables. 

This result will be useful, for example, in relating processes like 

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