(3+1)D dilute Glasma initial conditions in simulations of heavy-ion collisions

In this thesis, an approximation for the full (3+1)D dynamics of the Glasma is presented, which breaks boost-invariance on the level of the nuclear fields and leads to rapidity dependence in the final results. For this treatment, the Yang-Mills equations are linearized in covariant gauge, where lower-order, nonlinear contributions are neglected and the dynamics are captured by the (3+1)D dilute Glasma. The analytic solutions of the (3+1)D dilute Glasma are derived in both position and momentum space formulations, providing a comprehensive understanding of the involved (3+1)D dynamics. In position space, the field strength tensor results from the integration of free-streaming gluons that are produced in $2\rightarrow1$ scattering processes where the initial nuclear fields overlap. In momentum space, the event-averaged gluon number distribution for the (3+1)D dilute Glasma is derived in Coulomb gauge. A generalized, three-dimensional McLerran-Venugopalan nuclear model is developed for nuclei with realistic envelopes and intrinsic longitudinal correlations. Numerical results are presented for the rapidity structure of the energy-momentum tensor, the gluon number distribution, and the transverse energy of the (3+1)D dilute Glasma. In position space, the extended longitudinal collision geometry and finite longitudinal correlation length break boost-invariance. In momentum space, the results each follow universal parametrizations and are fixed by the values of two scaling parameters. Furthermore, the numerical results exhibit limiting fragmentation where the rapidity profiles approach a limiting distribution at large rapidities. This feature is also derived locally in position space for the analytic expressions of the field strength tensor and, in momentum space, for the transverse energy of the (3+1)D dilute Glasma.