{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/27998"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/27998","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"A gauge-invariant, symmetry-preserving truncation of JIMWLK","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).","abstract_html":"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_has_math":false,"creators":["Moerman, RobertWilliam"],"institution":"Department of Physics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Weigert, Heribert"],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018","date_published":"2018","updated_at":"2026-07-22T22:23:13Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/27998","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Weigert, Heribert"]},{"key":"dc:creator","label":"Author","values":["Moerman, RobertWilliam"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-05-07T14:24:16Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-05-07T14:24:16Z"]},{"key":"dc:date.issued","label":"Date","values":["2018"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Physics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/27998"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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)."]},{"key":"dc:title","label":"Title","values":["A gauge-invariant, symmetry-preserving truncation of JIMWLK"]}]}],"canonical_facts":{"dc:contributor.advisor":["Weigert, Heribert"],"dc:creator":["Moerman, RobertWilliam"],"dc:date.accessioned":["2018-05-07T14:24:16Z"],"dc:date.available":["2018-05-07T14:24:16Z"],"dc:date.issued":["2018"],"dc:description.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)."],"dc:identifier.uri":["http://hdl.handle.net/11427/27998"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Physics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["A gauge-invariant, symmetry-preserving truncation of JIMWLK"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:23:13Z"}