  Light-front quantization has important advantages for describing relativistic
statistical systems, particularly systems for which boost invariance is
essential, such as the fireball created in a heavy ion collisions. In this
paper we develop light-front field theory at finite temperature and density
with special attention to quantum chromodynamics. We construct the most general
form of the statistical operator allowed by the Poincare algebra and show that
there are no zero-mode related problems when describing phase transitions. We
then demonstrate a direct connection between densities in light-front thermal
field theory and the parton distributions measured in hard scattering
experiments. Our approach thus generalizes the concept of a parton distribution
to finite temperature. In light-front quantization, the gauge-invariant Green's
functions of a quark in a medium can be defined in terms of just 2-component
spinors and have a much simpler spinor structure than the equal-time fermion
propagator. From the Green's function, we introduce the new concept of a
light-front density matrix, whose matrix elements are related to forward and to
off-diagonal parton distributions. Furthermore, we explain how thermodynamic
quantities can be calculated in discretized light-cone quantization, which is
applicable at high chemical potential and is not plagued by the
fermion-doubling problem.
