  We have studied the exchange corrections to linear electrostatic wave
propagation in a plasma using a quantum kinetic formalism. Specifically we have
considered the zero temperature limit. In order to simplify the calculations we
have focused on the long wavelength limit, i.e. wavelengths much longer than
the de Broglie wavelength. For the case of ion-acoustic waves we have
calculated the exchange correction both to the damping rate and the real part
of the frequency. For Langmuir waves the frequency shift due to exchange
effects is found. Our results are compared with the frequency shifts deduced
from commonly used exchange potentials which are computed from density
functional theory.
