Physics 357
Set V Feynman Diagram
1a. Using the table in the notes for Mfi set up the expression for the following diagram representing the one
photon exchange between two electrons. In this electron-electron scattering diagram p1 and p2 are the
relativistic three momentum for the two incoming electrons and p3 and p4 are the relativistic three momentum
for the two outgoing electrons. Assume Electrons 1 and 3 have helicity = +1 and electrons 2 and 4 have
helicity = -1. Work in the center of mass frame and let p1 be along the z direction.
Mfi = [left outgoing state]{left vertex function}[left incoming state]{PROPAGATOR}[right outgoing state]{right vertex function}[right incoming state]
2. Multiply all the matrices and carry out the summations to obtain a final expression.
HINT: Note that in the final state (in center of mass system) the momenta of particles 3 (and 4) will make
an angle of θ (and θ + π) with the z direction (see diagram for problem set 3). The positive helicity state
for the new particle 3 direction will be given in terms of θ . The “rotated” spin matrix can be obtained
from a rotation about the y direction (y is perpendicular to scattering plane) as follows. ( α =1 and β = 0
are the components of positive helicity when p is along z):
cos( θ / 2) − sin( θ / 2) α  α'
 sin( θ / 2) cos( θ / 2)   β  =  β' 
     roatataed
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