provided we also interpret u(-k+) = v(k+) and v(-p_) = u{p_). This can be understood as a generalization of the Pauli principle which holds when identical particles exist in the initial and final states. The interchange is shown diagram-matically in Fig. 10.6. To use this symmetry, it is best to regard an incoming positron with four-momentum k+ as equivalent to an outgoing electron with four-nomentum -k+. From this point of view there are two outgoing electrons in this problem — one with four-momentum p_ and one with four-momentum -k+. Hence, it is expected that the amplitude should be antisymmetric under interchange of the two.

This sign arises naturally from the field theory reduction. For identical particles, the matrix element (10.66) must be replaced by two matrix elements:

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