{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23946"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23946","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Two applications of Berry's phase in fermionic field theory","abstract":"When quantized fermions are coupled to a background field , nontrivial effects may arise due to the geometry and/or topology of the space of background field configurations. In this thesis, two examples of Berry's geometrical phase in a fermionic sea are studied: the anomalous commutator in gauge field theory and the intrinsic orbital angular momentum in superftuid 3He-A. Chapter 1 is a brief introduction. Chapter 2 reviews Berry's Phase and several toy models. Effective actions are calculated for two models in gradient expansions and the role of a geometric term is discussed. Chapter 3 investigates the anomalous commutator in the generators of gauge symmetry in field theory. Using an idea introduced by Sonoda, the Berry phase of the vacuum state is found to be the sum of the Berry phases of the individual states in the sea plus a piece due to the infinite nature of the Dirac sea. The latter is the anomalous commutator. Also found is a relative minus sign between the commutator of the total gauge symmetry generators and the commutator of the fermionic charge generators. Examples are given. In Chapter 4, a geometric way of deriving the intrinsic orbital angular momentum term in the 3He-A equations of motion is presented. Homogeneous, adiabatically evolving textures at zero temperature are found to pick up a nonzero ground-state Berry phase, where the ground state is taken to be a filled sea of Bogoliubov quasiparticles. Interpreting the phase as a Wess-Zumino effective action for the condensate provides a geometric origin for the intrinsic angular momentum. The idea of a ground-state phase is then extended to other gap functions and a more general result is obtained. Chapter 5 concludes with a discussion of the possibility of unifying the two problems in a more general framework and directions for further work.","abstract_html":"When quantized fermions are coupled to a background field , nontrivial effects may arise due to the geometry and/or topology of the space of background field configurations. In this thesis, two examples of Berry's geometrical phase in a fermionic sea are studied: the anomalous commutator in gauge field theory and the intrinsic orbital angular momentum in superftuid 3He-A. Chapter 1 is a brief introduction. Chapter 2 reviews Berry's Phase and several toy models. Effective actions are calculated for two models in gradient expansions and the role of a geometric term is discussed. Chapter 3 investigates the anomalous commutator in the generators of gauge symmetry in field theory. Using an idea introduced by Sonoda, the Berry phase of the vacuum state is found to be the sum of the Berry phases of the individual states in the sea plus a piece due to the infinite nature of the Dirac sea. The latter is the anomalous commutator. Also found is a relative minus sign between the commutator of the total gauge symmetry generators and the commutator of the fermionic charge generators. Examples are given. In Chapter 4, a geometric way of deriving the intrinsic orbital angular momentum term in the 3He-A equations of motion is presented. Homogeneous, adiabatically evolving textures at zero temperature are found to pick up a nonzero ground-state Berry phase, where the ground state is taken to be a filled sea of Bogoliubov quasiparticles. Interpreting the phase as a Wess-Zumino effective action for the condensate provides a geometric origin for the intrinsic angular momentum. The idea of a ground-state phase is then extended to other gap functions and a more general result is obtained. Chapter 5 concludes with a discussion of the possibility of unifying the two problems in a more general framework and directions for further work.","abstract_has_math":false,"creators":["Goff, William Eugene"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Stone, Michael"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-18T17:31:56Z","date_published":"2011-05-18T17:31:56Z","updated_at":"2026-07-22T22:25:23Z","subjects":["Berry's phase","Fermionic field theory","Berry's geometrical phase","fermionic sea","anomalous commutator","intrinsic orbital angular momentum","superfluid"],"languages":["en"],"rights":["1989 William Eugene Goff"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["3473766"],"render_values":[{"text":"3473766","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23946","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Stone, Michael"]},{"key":"dc:creator","label":"Author","values":["Goff, William Eugene"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-18T17:31:56Z","10000-01-01","1989"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","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."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Berry's phase","Fermionic field theory","Berry's geometrical phase","fermionic sea","anomalous commutator","intrinsic orbital angular momentum","superfluid"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["1989 William Eugene Goff"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["3473766","http://hdl.handle.net/2142/23946"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["When quantized fermions are coupled to a background field , nontrivial effects may arise due to the geometry and/or topology of the space of background field configurations. In this thesis, two examples of Berry's geometrical phase in a fermionic sea are studied: the anomalous commutator in gauge field theory and the intrinsic orbital angular momentum in superftuid 3He-A. Chapter 1 is a brief introduction. Chapter 2 reviews Berry's Phase and several toy models. Effective actions are calculated for two models in gradient expansions and the role of a geometric term is discussed. Chapter 3 investigates the anomalous commutator in the generators of gauge symmetry in field theory. Using an idea introduced by Sonoda, the Berry phase of the vacuum state is found to be the sum of the Berry phases of the individual states in the sea plus a piece due to the infinite nature of the Dirac sea. The latter is the anomalous commutator. Also found is a relative minus sign between the commutator of the total gauge symmetry generators and the commutator of the fermionic charge generators. Examples are given. In Chapter 4, a geometric way of deriving the intrinsic orbital angular momentum term in the 3He-A equations of motion is presented. Homogeneous, adiabatically evolving textures at zero temperature are found to pick up a nonzero ground-state Berry phase, where the ground state is taken to be a filled sea of Bogoliubov quasiparticles. Interpreting the phase as a Wess-Zumino effective action for the condensate provides a geometric origin for the intrinsic angular momentum. The idea of a ground-state phase is then extended to other gap functions and a more general result is obtained. Chapter 5 concludes with a discussion of the possibility of unifying the two problems in a more general framework and directions for further work.","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-18T17:31:56Z No. of bitstreams: 1 1989_goff.pdf: 9072640 bytes, checksum: 6f95d719e143cd6b501cdde79f4fb28a (MD5)","Made available in DSpace on 2011-05-18T17:31:56Z (GMT). No. of bitstreams: 1 1989_goff.pdf: 9072640 bytes, checksum: 6f95d719e143cd6b501cdde79f4fb28a (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-18T17:31:56Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:15:01-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["Two applications of Berry's phase in fermionic field theory"]}]}],"canonical_facts":{"dc:contributor":["Stone, Michael"],"dc:creator":["Goff, William Eugene"],"dc:date":["2011-05-18T17:31:56Z","10000-01-01","1989"],"dc:description":["When quantized fermions are coupled to a background field , nontrivial effects may arise due to the geometry and/or topology of the space of background field configurations. In this thesis, two examples of Berry's geometrical phase in a fermionic sea are studied: the anomalous commutator in gauge field theory and the intrinsic orbital angular momentum in superftuid 3He-A. Chapter 1 is a brief introduction. Chapter 2 reviews Berry's Phase and several toy models. Effective actions are calculated for two models in gradient expansions and the role of a geometric term is discussed. Chapter 3 investigates the anomalous commutator in the generators of gauge symmetry in field theory. Using an idea introduced by Sonoda, the Berry phase of the vacuum state is found to be the sum of the Berry phases of the individual states in the sea plus a piece due to the infinite nature of the Dirac sea. The latter is the anomalous commutator. Also found is a relative minus sign between the commutator of the total gauge symmetry generators and the commutator of the fermionic charge generators. Examples are given. In Chapter 4, a geometric way of deriving the intrinsic orbital angular momentum term in the 3He-A equations of motion is presented. Homogeneous, adiabatically evolving textures at zero temperature are found to pick up a nonzero ground-state Berry phase, where the ground state is taken to be a filled sea of Bogoliubov quasiparticles. Interpreting the phase as a Wess-Zumino effective action for the condensate provides a geometric origin for the intrinsic angular momentum. The idea of a ground-state phase is then extended to other gap functions and a more general result is obtained. Chapter 5 concludes with a discussion of the possibility of unifying the two problems in a more general framework and directions for further work.","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-18T17:31:56Z No. of bitstreams: 1 1989_goff.pdf: 9072640 bytes, checksum: 6f95d719e143cd6b501cdde79f4fb28a (MD5)","Made available in DSpace on 2011-05-18T17:31:56Z (GMT). No. of bitstreams: 1 1989_goff.pdf: 9072640 bytes, checksum: 6f95d719e143cd6b501cdde79f4fb28a (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-18T17:31:56Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:15:01-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Thesis","U of I Only"],"dc:identifier":["3473766","http://hdl.handle.net/2142/23946"],"dc:language":["en"],"dc:rights":["1989 William Eugene Goff"],"dc:subject":["Berry's phase","Fermionic field theory","Berry's geometrical phase","fermionic sea","anomalous commutator","intrinsic orbital angular momentum","superfluid"],"dc:title":["Two applications of Berry's phase in fermionic field theory"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:23Z"}