Light-front Hamiltonian jet evolution in the Glasma

We develop a light-front Hamiltonian formalism to study the real-time quantum evolution of a high-energy quark propagating through the Glasma phase of a heavy-ion collision. In this work, the quark Fock space is truncated to the $\ket{q}$ sector and the wavefunction is expanded in a discrete basis representation, following the time-dependent Basis Light-Front Quantization (tBLFQ) framework. The classical Glasma background fields enter as a time-dependent external potential, and physical observables are extracted as expectation values of quantum operators over the time-evolved state. We compute the transverse momentum broadening and the jet quenching parameter, finding results consistent with classical estimates, including the expected scaling with respect to the saturation momentum, and use them to perform phenomenological estimations for different collision systems. We also study the color rotation of the quark state induced by the Glasma fields, and examine its dependence on the saturation scale and the gauge choice. This formalism allows systematic improvements to include, in particular, non-eikonal propagation and parton splittings that will be considered in forthcoming publications.