  We apply classical gluodynamics to early stages of ultrarelativistic
heavy-ion collisions. We start by going through the space-time evolution of
ultrarelativistic heavy-ion collisions in the color glass condensate framework
and the basics of real-time gluodynamics on the lattice in the temporal gauge.
  We study the plasmon mass scale in three- and two-dimensional systems by
comparing three different methods to measure the mass scale. The methods are a
formula which can be derived from Hard Thermal Loop effective theory at leading
order (HTL), the effective dispersion relation (DR) and measurement of the
plasma oscillation frequency triggered by the introduction of a uniform
electric field (UE) into the system. We observe that in both systems the
plasmon mass scale decreases like a power law after an occupation number
dependent initial transient time. In both cases the UE and HTL methods are in
rough agreement, and in the three-dimensional case the two agree in the
continuum limit.
  As a second way to study the quasiparticle properties, we derive, implement
and test an algorithm which can be used to simulate linearized fluctuations on
top of the classical background. The algorithm is derived by requiring
conservation of Gauss' law and gauge invariance. We then apply the algorithm to
spectral properties of overoccupied gluodynamics using linear response theory.
We establish the existence of transverse and longitudinal quasiparticles by
extracting their spectral functions. We also extract the dispersion relation,
effective mass, plasmon mass and damping rate of the quasiparticles. Our
results are consistent with the HTL effective theory, but we also observe
effects beyond leading order HTL.
