),Interaction with the Electromagnetic Field
The presence of an electromagnetic field adds
the interaction term, (superscript),
(7)
which is the action of the electromagnetic Lorentz
force. This is the quantum mechanical Bohm-Aharonov Effect,
where 
is
the charge and 
is the electromagnetic gauge potential. In the
absence of a magnetic field this becomes,
(8)
The affect on the probability wave function is once again the addition of an interaction phase factor.
(9)
The phase shift added to the propagator in a static electro-gravitic field is then,
(10)
This shows that both the gravitational field and electromagnetic field act upon the propagator in the same manner. Both induce a phase shift which causes the wave function to disperse in the direction which minimizes the action, thereby decreasing the relative energy of the wave. The difference is that the gravitational field contribution is the result of the mass/energy, and the electromagnetic field contribution is a result of the electromagnetic energy. Both fields are representative of the local environment of a test particle.