  Three-dimensional quantum electrodynamics exhibits a number of interesting
properties, such as dynamical chiral symmetry breaking, weak confinement, and
non-Fermi liquid behavior, and also has wide applications in condensed matter
physics. We study the effects of random potentials, which exist in almost all
realistic condensed-matter systems, on the low-energy behaviors of massless
Dirac fermions by means of renormalization group method, and show that the role
of random mass is significantly enhanced by the gauge interaction, whereas
random scalar and vector potentials are insusceptible to the gauge interaction
at the one-loop order. The static random potential breaks the Lorentz
invariance, and as such induces unusual renormalization of fermion velocity. We
then consider the case in which three types of random potentials coexist in the
system. The random scalar potential is found to play a dominant role in the
low-energy region, and drives the system to undergo a quantum phase transition.
