Amplitude of Vertex Diagram: Unchanged?

[noether21]

If the momenta on the three external legs p(incoming fermion), p'(outgoing fermion) and
p-p' (photon) of a vertex diagram are replaced by -p, -p' and p'-p respectively (i.e., all the external momenta are multiplied by -1) does the amplitude remain unchanged?

 

[malawi_glenn]

yes due to crossing symmetry

 

[noether21]

The analytic continuation argument used to derive crossing symmetry (Itzykson & Zuber)
seems to require that there are no massless particles (vacuum is an isolated point). Further
it appears that the external legs must be on mass-shell in the crossing symmetry derivation.
In the 3-point vertex function all the external legs cannot be on mass-shell. I think the
answer to the question is still yes, but short of a lengthy analytic continuation argument
that handles massless particles and doesn't require mass-shell condition (which may not even work), it's unclear how crossing symmetry can be applied directly. Any thoughts?

 

[malawi_glenn]

ah yes, a photon is involved, didn't thought of that =/