Simulations of the Glasma in 3+1D

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.