Kinetic and canonical momentum broadening in the Glasma

TL;DR

This paper develops a quantum formalism for particle evolution in the Glasma, highlighting gauge invariance in momentum definitions and analyzing momentum broadening effects in heavy-ion collisions.

Contribution

It establishes a connection between classical Wong's equations and quantum equations of motion, introducing a gauge-invariant kinetic momentum and optimizing numerical methods.

Findings

Kinetic momentum broadening includes contributions from transverse fields.

Imposing a transverse Coulomb gauge reduces numerical errors.

The formalism links classical and quantum descriptions of particle dynamics.

Abstract

We lay the foundations for a quantum formalism describing the real-time evolution of particles in the Glasma phase of a heavy-ion collision, focusing on the implications of gauge invariance in the definition of the momentum of a particle in a classical background field. We first establish the correspondence between the classical Wong's equations and the Heisenberg equations of motion for a particle in a classical non-Abelian background field. Using this correspondence, we obtain equations of motion for both the kinetic momentum -- the gauge invariant, physically measurable quantity -- and the canonical momentum, which is conjugate to the coordinates in the Hamiltonian. In particular, the kinetic momentum broadening receives non-trivial contributions from the transverse field components, even in the eikonal limit. Finally, we demonstrate that imposing a transverse Coulomb gauge condition at the initial time significantly reduces the accumulation of numerical errors, thereby providing an optimized framework for the forthcoming quantum implementation.