A gauge-invariant, symmetry-preserving truncation of JIMWLK
type: CreativeWork
description: The colour glass condensate captures quantum chromodynamics in its application to high-energy collider experiments in the spirit of an effective field theory. In deeply inelastic lepton-hadron scattering experiments, as well as in hadron-hadron collisions, the internal degrees of freedom of in-state hadrons are dominated by a dense medium of gluonic matter called the colour glass condensate. Interactions with this medium by some (dilute) probe are most naturally described in terms of Wilson-lines and their correlators. The energy-dependence of these correlators is given by the JIMWLK (Jalilian-Marian+Iancu+McLerran+Weigert+Leonidov+Kovner) equa- tion which, when applied to a correlator, generates an infinite tower of coupled Dyson-Schwinger- like equations referred to as a Balitsky Hierarchy. In this thesis, I present a novel method for truncating, in a gauge-invariant and symmetry- preserving manner, the Balitsky hierarchy associated with matrices of Wilson-line correlators. This truncation is realized by parameterizing the energy-dependence of the symmetric and anti- symmetric parts of these matrices independently via energy-evolution operators which evolve ini- tial conditions in a manner akin to the time-evolution of Hermitian operators in the Heisenberg picture of quantum mechanics. These energy-evolution operators are path-ordered exponentials whose exponents are expanded in terms of energy-dependent "colour structure functions". I show how the properties of contributions to the expansion of these exponents (at each order in the expansion) are constrained by the group theory of SU(Nc).
abstract: The colour glass condensate captures quantum chromodynamics in its application to high-energy collider experiments in the spirit of an effective field theory. In deeply inelastic lepton-hadron scattering experiments, as well as in hadron-hadron collisions, the internal degrees of freedom of in-state hadrons are dominated by a dense medium of gluonic matter called the colour glass condensate. Interactions with this medium by some (dilute) probe are most naturally described in terms of Wilson-lines and their correlators. The energy-dependence of these correlators is given by the JIMWLK (Jalilian-Marian+Iancu+McLerran+Weigert+Leonidov+Kovner) equa- tion which, when applied to a correlator, generates an infinite tower of coupled Dyson-Schwinger- like equations referred to as a Balitsky Hierarchy. In this thesis, I present a novel method for truncating, in a gauge-invariant and symmetry- preserving manner, the Balitsky hierarchy associated with matrices of Wilson-line correlators. This truncation is realized by parameterizing the energy-dependence of the symmetric and anti- symmetric parts of these matrices independently via energy-evolution operators which evolve ini- tial conditions in a manner akin to the time-evolution of Hermitian operators in the Heisenberg picture of quantum mechanics. These energy-evolution operators are path-ordered exponentials whose exponents are expanded in terms of energy-dependent "colour structure functions". I show how the properties of contributions to the expansion of these exponents (at each order in the expansion) are constrained by the group theory of SU(Nc).
author: Moerman, RobertWilliam
language: eng
date published: 2018
date modified: 2026-07-22T22:23:13Z
provider: University of Cape Town
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Department of Physics

PropertyValue
property ID: Handle
value: http://hdl.handle.net/11427/27998