  The Glasma is a gluonic state of matter which can be created in collisions of
relativistic heavy ions and is a precursor to the quark-gluon plasma. The
existence of this state is a prediction of the color glass condensate (CGC)
effective theory. In many applications of the CGC framework, the boost
invariant approximation is employed. It assumes that the longitudinal extent of
the nuclei can be approximated as infinitesimally thin. Consequently, the
Glasma produced from such a collision is boost invariant and can be effectively
described in 2+1D. Therefore, observables of the boost invariant Glasma are by
construction independent of rapidity.
  The main goal of this thesis is to develop a numerical method for the
non-boost-invariant setting where nuclei are assumed to be thin, but of finite
longitudinal extent. This is in conflict with a number of simplifications that
are used in the boost invariant case. In particular, one has to describe the
collisions in 3+1D in the laboratory or center-of-mass frame. The change of
frame forces the explicit inclusion of the color charges of nuclei. The new
method is tested using an extension of the McLerran-Venugopalan model which
includes a parameter for longitudinal thickness. It reproduces the boost
invariant setting as a limiting case. Studying the pressure components of the
Glasma, one finds the pressure anisotropy remains large. The energy density of
the Glasma depends on rapidity due to the explicit breaking of boost
invariance. The width of the observed rapidity profiles is controlled by the
collision energy and can be shown to roughly agree with experimental data.
Finally, a new numerical scheme for real-time lattice gauge theory is developed
which provides higher numerical stability than the previous method. This new
scheme is shown to be gauge-covariant and conserves the Gauss constraint even
for large time steps.
