{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19861"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19861","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A field theory for the fractional quantum Hall effect","abstract":"In this thesis we derive a field theory approach to the Fractional Quantum Hall Effect (FQHE). The goal is to develop a field theory for a system of interacting electrons moving in a plane in the presence of an external magnetic field, in the hope that the FQHE states will appear naturally as the semiclassical states of the theory. In this framework, the FQHE states are understood as infrared stable fixed points, and the long distance, low energy properties of the system should be described exactly by this theory.","abstract_html":"In this thesis we derive a field theory approach to the Fractional Quantum Hall Effect (FQHE). The goal is to develop a field theory for a system of interacting electrons moving in a plane in the presence of an external magnetic field, in the hope that the FQHE states will appear naturally as the semiclassical states of the theory. In this framework, the FQHE states are understood as infrared stable fixed points, and the long distance, low energy properties of the system should be described exactly by this theory.","abstract_has_math":false,"creators":["Lopez, Ana Maria"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Fradkin, Eduardo H."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:21:00Z","date_published":"2011-05-07T12:21:00Z","updated_at":"2026-07-22T22:25:14Z","subjects":["Physics, Condensed Matter"],"languages":["eng"],"rights":["Copyright 1994 Lopez, Ana Maria"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9512468","(UMI)AAI9512468"],"render_values":[{"text":"AAI9512468","href":null,"code":true},{"text":"(UMI)AAI9512468","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19861","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Fradkin, Eduardo H."]},{"key":"dc:creator","label":"Author","values":["Lopez, Ana Maria"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:21:00Z","10000-01-01","1994"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Physics, Condensed Matter"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1994 Lopez, Ana Maria"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9512468","(UMI)AAI9512468","http://hdl.handle.net/2142/19861"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis we derive a field theory approach to the Fractional Quantum Hall Effect (FQHE). The goal is to develop a field theory for a system of interacting electrons moving in a plane in the presence of an external magnetic field, in the hope that the FQHE states will appear naturally as the semiclassical states of the theory. In this framework, the FQHE states are understood as infrared stable fixed points, and the long distance, low energy properties of the system should be described exactly by this theory.","We show the existence of an exact equivalence between a system of interacting electrons, and a system of fermions tightly bound to infinitesimal solenoids carrying a statistical magnetic flux. These are the fermionic Chern-Simons gauge field theories. The transformed system can be studied using standard techniques of perturbation theory, because its ground state, at the mean field level, is nondegenerate and has a gap to all the excitations. The power of this theory resides in the fact that it allows for a systematic calculation of the properties of the FQHE states around a mean-field ground state which has a gap.","We consider in detail the fluid states in which the mean-field theory replaces the statistical fluxes by an average statistical magnetic field, i.e., the Average Field Approximation. We calculate the electromagnetic response functions within the semiclassical approximation, and determine the spectrum of collective excitations. We derive the ground state wave function directly from the field theory, and, as expected, we find the Laughlin wave function for the states with filling fraction $\\nu$ = ${1\\over m}$. We show that the universal properties of the Laughlin wave functions are a consequence of general principles, i.e., incompressibility, and Galilean and gauge invariance, which determine the analytic structure of the equal-time density correlation functions at long distances. Finally, we generalize our approach to study the FQHE in double-layer systems.","Made available in DSpace on 2011-05-07T12:21:00Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9512468.pdf: 8959117 bytes, checksum: bd1d7884a300f2bb83cac202d3cddf2e (MD5) Previous issue date: 1994","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:39:56Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:16:57-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["A field theory for the fractional quantum Hall effect"]}]}],"canonical_facts":{"dc:contributor":["Fradkin, Eduardo H."],"dc:creator":["Lopez, Ana Maria"],"dc:date":["2011-05-07T12:21:00Z","10000-01-01","1994"],"dc:description":["In this thesis we derive a field theory approach to the Fractional Quantum Hall Effect (FQHE). The goal is to develop a field theory for a system of interacting electrons moving in a plane in the presence of an external magnetic field, in the hope that the FQHE states will appear naturally as the semiclassical states of the theory. In this framework, the FQHE states are understood as infrared stable fixed points, and the long distance, low energy properties of the system should be described exactly by this theory.","We show the existence of an exact equivalence between a system of interacting electrons, and a system of fermions tightly bound to infinitesimal solenoids carrying a statistical magnetic flux. These are the fermionic Chern-Simons gauge field theories. The transformed system can be studied using standard techniques of perturbation theory, because its ground state, at the mean field level, is nondegenerate and has a gap to all the excitations. The power of this theory resides in the fact that it allows for a systematic calculation of the properties of the FQHE states around a mean-field ground state which has a gap.","We consider in detail the fluid states in which the mean-field theory replaces the statistical fluxes by an average statistical magnetic field, i.e., the Average Field Approximation. We calculate the electromagnetic response functions within the semiclassical approximation, and determine the spectrum of collective excitations. We derive the ground state wave function directly from the field theory, and, as expected, we find the Laughlin wave function for the states with filling fraction $\\nu$ = ${1\\over m}$. We show that the universal properties of the Laughlin wave functions are a consequence of general principles, i.e., incompressibility, and Galilean and gauge invariance, which determine the analytic structure of the equal-time density correlation functions at long distances. Finally, we generalize our approach to study the FQHE in double-layer systems.","Made available in DSpace on 2011-05-07T12:21:00Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9512468.pdf: 8959117 bytes, checksum: bd1d7884a300f2bb83cac202d3cddf2e (MD5) Previous issue date: 1994","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:39:56Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:16:57-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9512468","(UMI)AAI9512468","http://hdl.handle.net/2142/19861"],"dc:language":["eng"],"dc:rights":["Copyright 1994 Lopez, Ana Maria"],"dc:subject":["Physics, Condensed Matter"],"dc:title":["A field theory for the fractional quantum Hall effect"],"dc:type":["text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:14Z"}