{"doi":"10.17077/etd.2ohjut0a","title":"The diffeomorphism field","abstract":"<jats:p>&lt;p&gt;The diffeomorphism field is introduced to the physics literature in [1] where it                 arises as a background field coupled to Polyakov’s quantum gravity in two                 dimensions, where Einstein’s gravity is trivial. Moreover, it is seen in many ways                 as the gravitational analog of the Yang-Mills field. This raises the question of                 whether the diffeomorphism field exists in higher dimensions, playing an essential                 role in gravity either by supplementing Einstein’s theory or by modifying it.&lt;/p&gt;&lt;p&gt;With this motivation, several distinct theories governing the dynamics of the                 diffeomorphism field have been constructed and developed by mimicking the                 construction of the Yang-Mills theory from the Kac-Moody algebra. This analogy,                 however, is not perfect and there are many subtleties and difficulties encountered.&lt;/p&gt;&lt;p&gt;This thesis constitutes a further development. The previously proposed theories are                 carefully examined; certain subtleties and problems in them have been discovered and                 made apparent. Some of these problems have been solved, and for others possible                 routes to follow have been laid down. Finally, other geometric approaches than the                 ones followed before are investigated.&lt;/p&gt;</jats:p>","journal":null,"year":null,"id":600080,"datarank":0.10397207708399181,"base_score":0.6931471805599453,"endowment":0.6931471805599453,"self_citation_contribution":0.10397207708399181,"citation_network_contribution":0.0,"self_endowment_contribution":0.10397207708399181,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":1,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1538230,"name":"Delalcan Kilic","orcid":null,"position":1,"is_corresponding":false},{"id":1538232,"name":"Vincent G. Rodgers","orcid":null,"position":2,"is_corresponding":false},{"id":1179253,"name":"Yannick Meurice","orcid":"0000-0002-0995-9694","position":3,"is_corresponding":false},{"id":1538234,"name":"Wayne Nicholas Polyzou","orcid":null,"position":4,"is_corresponding":false},{"id":117239,"name":"Hao Fang","orcid":"0000-0002-2879-5146","position":5,"is_corresponding":false},{"id":1538235,"name":"Yasar Onel","orcid":null,"position":6,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"resolved":true,"title":"The diffeomorphism field","abstract":"&lt;p&gt;The diffeomorphism field is introduced to the physics literature in [1] where it arises as a background field coupled to Polyakov’s quantum gravity in two dimensions, where Einstein’s gravity is trivial. Moreover, it is seen in many ways as the gravitational analog of the Yang-Mills field. This raises the question of whether the diffeomorphism field exists in higher dimensions, playing an essential role in gravity either by supplementing Einstein’s theory or by modifying it.&lt;/p&gt;&lt;p&gt;With this motivation, several distinct theories governing the dynamics of the diffeomorphism field have been constructed and developed by mimicking the construction of the Yang-Mills theory from the Kac-Moody algebra. This analogy, however, is not perfect and there are many subtleties and difficulties encountered.&lt;/p&gt;&lt;p&gt;This thesis constitutes a further development. The previously proposed theories are carefully examined; certain subtleties and problems in them have been discovered and made apparent. Some of these problems have been solved, and for others possible routes to follow have been laid down. Finally, other geometric approaches than the ones followed before are investigated.&lt;/p&gt;","is_dataset_classified":null,"base_score":0.6931471805599453,"endowment":0.6931471805599453,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"23304386","pmcid":null,"openalex_id":"https://openalex.org/W2891397405","authors":[],"funders":[],"total_grants":0,"fwci":null,"citation_percentile":null,"influential_citations":0,"citation_trend":[{"year":2019,"count":1}],"oa_status":"green","license":null,"oa_locations":[{"url":"https://ir.uiowa.edu/cgi/viewcontent.cgi?article=7713&context=etd","host_type":"repository"},{"url":"https://ir.uiowa.edu/cgi/viewcontent.cgi?article=7713&context=etd","host_type":"repository"},{"url":"https://ir.uiowa.edu/etd/6156","host_type":"repository"},{"url":"https://doi.org/10.17077/etd.2ohjut0a","host_type":""}],"fields_of_study":["Black Holes and Theoretical Physics","Cosmology and Gravitation Theories","Noncommutative and Quantum Gravity Theories"],"mesh_terms":[],"keywords":["Diffeomorphism","Field (mathematics)","Gravitational field","Physics","Gravitation","Pure mathematics","Algebra over a field","Theoretical physics","Mathematics","Classical mechanics"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-07-29T12:10:49.446143Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}