{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19406"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19406","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Bosonization in 1 + 1/2 dimensions","abstract":"In this thesis we derive a set of bosonization rules for the problem of a fermionic interacting system living on the half line coupled to a quantum degree of freedom at a boundary. This is an appropriate model to describe the physics of an electronic system in quantum wires with impurities. First we derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green's function and determine the effects of the boundaries on its analytic structure.","abstract_html":"In this thesis we derive a set of bosonization rules for the problem of a fermionic interacting system living on the half line coupled to a quantum degree of freedom at a boundary. This is an appropriate model to describe the physics of an electronic system in quantum wires with impurities. First we derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green's function and determine the effects of the boundaries on its analytic structure.","abstract_has_math":false,"creators":["Fuentes, Manuel Alejandro"],"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":"2011-05-07T12:06:32Z","date_published":"2011-05-07T12:06:32Z","updated_at":"2026-07-22T22:25:12Z","subjects":["Physics, Condensed Matter"],"languages":["eng"],"rights":["Copyright 1995 Fuentes, Manuel Alejandro"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9624347","(UMI)AAI9624347"],"render_values":[{"text":"AAI9624347","href":null,"code":true},{"text":"(UMI)AAI9624347","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19406","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":["Fuentes, Manuel Alejandro"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:06:32Z","10000-01-01","1995"]},{"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 1995 Fuentes, Manuel Alejandro"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9624347","(UMI)AAI9624347","http://hdl.handle.net/2142/19406"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis we derive a set of bosonization rules for the problem of a fermionic interacting system living on the half line coupled to a quantum degree of freedom at a boundary. This is an appropriate model to describe the physics of an electronic system in quantum wires with impurities. First we derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green's function and determine the effects of the boundaries on its analytic structure.","We also consider a system of free fermions in the half line coupled to a backscattering amplitude at the boundary. We calculate the exact effective action for general backscattering amplitudes. The action also includes the effects of both a (time-dependent) forward scattering amplitude and a dynamical chiral twist of the fermion boundary conditions. For a small backscattering amplitude, the effective action has the expected boundary Sine-Gordon form. We discuss applications of our results to one-dimensional Fermi systems with local backscattering.","Finally, we study the Luttinger-Thirring model in one space dimension coupled to a quantum impurity at the origin. We generalize the bosonization methods developed for the free fermions, to study the effects of interactions on fermi systems coupled to impurities. Special attention is given to the role of the fermion boundary conditions on the bosonized effective theory. We apply our results to the study of the induced charge at the boundary. Using this result, we analyze the interplay between the boundary degree of freedom and the interaction. We give detail discussion of the properties of the one- particle green function (relevant for tunneling problems).","Made available in DSpace on 2011-05-07T12:06:32Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9624347.pdf: 4282008 bytes, checksum: 724edcf876bdc87331bd227daa6765d0 (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:36:44Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:14:56-05:00 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":["Bosonization in 1 + 1/2 dimensions"]}]}],"canonical_facts":{"dc:contributor":["Fradkin, Eduardo H."],"dc:creator":["Fuentes, Manuel Alejandro"],"dc:date":["2011-05-07T12:06:32Z","10000-01-01","1995"],"dc:description":["In this thesis we derive a set of bosonization rules for the problem of a fermionic interacting system living on the half line coupled to a quantum degree of freedom at a boundary. This is an appropriate model to describe the physics of an electronic system in quantum wires with impurities. First we derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green's function and determine the effects of the boundaries on its analytic structure.","We also consider a system of free fermions in the half line coupled to a backscattering amplitude at the boundary. We calculate the exact effective action for general backscattering amplitudes. The action also includes the effects of both a (time-dependent) forward scattering amplitude and a dynamical chiral twist of the fermion boundary conditions. For a small backscattering amplitude, the effective action has the expected boundary Sine-Gordon form. We discuss applications of our results to one-dimensional Fermi systems with local backscattering.","Finally, we study the Luttinger-Thirring model in one space dimension coupled to a quantum impurity at the origin. We generalize the bosonization methods developed for the free fermions, to study the effects of interactions on fermi systems coupled to impurities. Special attention is given to the role of the fermion boundary conditions on the bosonized effective theory. We apply our results to the study of the induced charge at the boundary. Using this result, we analyze the interplay between the boundary degree of freedom and the interaction. We give detail discussion of the properties of the one- particle green function (relevant for tunneling problems).","Made available in DSpace on 2011-05-07T12:06:32Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9624347.pdf: 4282008 bytes, checksum: 724edcf876bdc87331bd227daa6765d0 (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:36:44Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:14:56-05:00 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":["AAI9624347","(UMI)AAI9624347","http://hdl.handle.net/2142/19406"],"dc:language":["eng"],"dc:rights":["Copyright 1995 Fuentes, Manuel Alejandro"],"dc:subject":["Physics, Condensed Matter"],"dc:title":["Bosonization in 1 + 1/2 dimensions"],"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":"2026-07-22T22:25:12Z"}