The Helicity density matrices provide statistical descriptions of the spin configurations of beam, target, scattered and recoil particles. The dynamics of the interaction are contained within the reduced S-matrix for individual before and after helicity states. For given spins and momenta an amplitude may therefore be defined,
This is compressed to the helicity amplitude notation,
with suppressed energy dependence. Calculating the EM amplitude for two fermions in the single virtual photon exchange approximation and according to the Feynman rules of quantum field interactions,
where 
and
and 
are the respective fermion currents between these
initial and final momentum and spin states.
A significant problem at this point is the nature of the currents evaluated at a 
vertex. The approximate
point coupling, where 
, is clearly modified due to the strong interaction. It is not possible to evaluate these effects
directly but applying the principles of current conservation and Lorentz invariance, it is possible to
constrain the form of these corrections and establish
experimentally measurable quantities.
Applying the Lorentz invariance condition to a matrix element the current may be written,
where 
represents 
matrix functions of the available independent 4-vectors 
and the 
-matrices, with the factor
i e extracted for normalisation purposes.
The matrix 
may be expressed as a linear combination of,
By appeal to the Dirac equations,
all but 
, 
, and 
may be ignored as they can be expressed as linear combinations of these
three.
Therefore, without loss of generality, the current may written,
The Hermitian property of 
demands that 
and 
must all be real functions.
The conservation of electro-magnetic current demands,
and for plane wave states with 
_i 
with the particle helicities 12 +/- $ corresponding
to the suffixes of the $H__A'_B';_A_B$ notation and where the order of particles is $<scat,recoilbeam,targ>$, $M$ representing the reduced S-matrix element. A factor of $2s$ is removed in defining the $_i$ amplitudes for later convenience.
In terms of the Mandelstam parameters [19]
s=(p_A+p_B)^(p_A+p_B)_
t=q^q_=- k^2sin^2( 
/2)
u=(p_A-p_D)^(p_A-p_D)_
and adopting a high energy approximation where
m is neglected with respect to 
, and 
is neglected with respect to m, the full EM amplitudes assume the form
where 
is now factored out of 
to give the normalization 
.