  This thesis reports on work undertaken in comparing the effects of the
phenomenon of radiation reaction in classical and quantum theories of
electrodynamics. Specifically, it is concerned with the prediction of the
change in position of a particle due to the inclusion of the self-force in the
theory. We calculate this position shift for the classical theory, treating
radiation reaction as a perturbation in line with the reduction of order
procedure. We calculate the contributions to the position shift in the
$\hbar\to 0$ limit of quantum field theory to order $e^2$ in the coupling, the
order of the classical self-force. These calculations contain the emission and
forward scattering one loop processes of quantum electrodynamics. The quantum
calculations are completed for the case of a particle represented by a scalar
field wave packet and then for a particle represented by the Dirac spinor
field. We additionally give an alternative derivation of the scalar results
using the interpretation of radiation reaction via a Green's function
decomposition, in order to explain and contrast the results achieved.
