{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/25062"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/25062","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On the construction of macroscopically local relativistic quantum theories","abstract":"\"The problem of providing a physical interpretation of a relativistic quantum theory is discussed. It is shown that a single operator corresponding to a localized measurement on the states of the-theory is sufficient for a significant part (perhaps all) of this interpretation. The application of this method of interpretation to the relativistic quantum theory defined on the representation space of an irreducible representation of a higher symmetry group containing the Poincare group is discussed. It is concluded that the higher symmetry is, in fact, of little use for this interpretation. This .leads in a natural way to the problem of finding some of these \"\"quasilocal\"\" operators on the space of states of a given relativistic quantum theory. 1'/ This problem is specialized to the problem of constructing a model relativistic quantum theory of a certain type. The procedure used is to attempt to construct a representation of the generators of the Poincare group on the Fock space X of real scalarbosons in such a way that quasilocal observables are easily expressible in terms of the canonical creation-destruction operators. The structure of the model permits the construction of the generators to be approached by successively satisfying their structure relations in each of the spaces ~(n) specified by the eigenvalues of the free field particle number operator. These structure relations are satisfied in~(l) and~(2). The mathematical details of the problem increase rapidly with n, and no explicit solution is obtained for n > 2. Arguments are given which make it plausible that the structure relations in~(n), with n> 2, may be satisfied by a large class of generators. Several trial solutions in the space ~(3) are described, and the difficulties associated with them are discussed.\"","abstract_html":""The problem of providing a physical interpretation of a relativistic quantum theory is discussed. It is shown that a single operator corresponding to a localized measurement on the states of the-theory is sufficient for a significant part (perhaps all) of this interpretation. The application of this method of interpretation to the relativistic quantum theory defined on the representation space of an irreducible representation of a higher symmetry group containing the Poincare group is discussed. It is concluded that the higher symmetry is, in fact, of little use for this interpretation. This .leads in a natural way to the problem of finding some of these ""quasilocal"" operators on the space of states of a given relativistic quantum theory. 1'/ This problem is specialized to the problem of constructing a model relativistic quantum theory of a certain type. The procedure used is to attempt to construct a representation of the generators of the Poincare group on the Fock space X of real scalarbosons in such a way that quasilocal observables are easily expressible in terms of the canonical creation-destruction operators. The structure of the model permits the construction of the generators to be approached by successively satisfying their structure relations in each of the spaces ~(n) specified by the eigenvalues of the free field particle number operator. These structure relations are satisfied in~(l) and~(2). The mathematical details of the problem increase rapidly with n, and no explicit solution is obtained for n > 2. Arguments are given which make it plausible that the structure relations in~(n), with n> 2, may be satisfied by a large class of generators. Several trial solutions in the space ~(3) are described, and the difficulties associated with them are discussed."","abstract_has_math":false,"creators":["Nance, Jon Roland"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Haag, R."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-31T15:21:22Z","date_published":"2011-05-31T15:21:22Z","updated_at":"2026-07-22T22:25:24Z","subjects":["macroscopically local relativistic quantum theory","relativistic quantum theory","field theory","scattering theory","quasilocal observables","scalar boson model"],"languages":["en"],"rights":["1966 Jon Roland Nance"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["6128057"],"render_values":[{"text":"6128057","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/25062","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Haag, R."]},{"key":"dc:creator","label":"Author","values":["Nance, Jon Roland"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-31T15:21:22Z","10000-01-01","1966"]},{"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":["macroscopically local relativistic quantum theory","relativistic quantum theory","field theory","scattering theory","quasilocal observables","scalar boson model"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["1966 Jon Roland Nance"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["6128057","http://hdl.handle.net/2142/25062"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"The problem of providing a physical interpretation of a relativistic quantum theory is discussed. It is shown that a single operator corresponding to a localized measurement on the states of the-theory is sufficient for a significant part (perhaps all) of this interpretation. The application of this method of interpretation to the relativistic quantum theory defined on the representation space of an irreducible representation of a higher symmetry group containing the Poincare group is discussed. It is concluded that the higher symmetry is, in fact, of little use for this interpretation. This .leads in a natural way to the problem of finding some of these \"\"quasilocal\"\" operators on the space of states of a given relativistic quantum theory. 1'/ This problem is specialized to the problem of constructing a model relativistic quantum theory of a certain type. The procedure used is to attempt to construct a representation of the generators of the Poincare group on the Fock space X of real scalarbosons in such a way that quasilocal observables are easily expressible in terms of the canonical creation-destruction operators. The structure of the model permits the construction of the generators to be approached by successively satisfying their structure relations in each of the spaces ~(n) specified by the eigenvalues of the free field particle number operator. These structure relations are satisfied in~(l) and~(2). The mathematical details of the problem increase rapidly with n, and no explicit solution is obtained for n > 2. Arguments are given which make it plausible that the structure relations in~(n), with n> 2, may be satisfied by a large class of generators. Several trial solutions in the space ~(3) are described, and the difficulties associated with them are discussed.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-31T15:21:22Z No. of bitstreams: 1 1966_nance.pdf: 2230808 bytes, checksum: 9b2bd845dc8e12b3d7bbb294e3840fbf (MD5)","Made available in DSpace on 2011-05-31T15:21:22Z (GMT). No. of bitstreams: 1 1966_nance.pdf: 2230808 bytes, checksum: 9b2bd845dc8e12b3d7bbb294e3840fbf (MD5) Previous issue date: 1966","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-31T15:21:22Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:11:24-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["On the construction of macroscopically local relativistic quantum theories"]}]}],"canonical_facts":{"dc:contributor":["Haag, R."],"dc:creator":["Nance, Jon Roland"],"dc:date":["2011-05-31T15:21:22Z","10000-01-01","1966"],"dc:description":["\"The problem of providing a physical interpretation of a relativistic quantum theory is discussed. It is shown that a single operator corresponding to a localized measurement on the states of the-theory is sufficient for a significant part (perhaps all) of this interpretation. The application of this method of interpretation to the relativistic quantum theory defined on the representation space of an irreducible representation of a higher symmetry group containing the Poincare group is discussed. It is concluded that the higher symmetry is, in fact, of little use for this interpretation. This .leads in a natural way to the problem of finding some of these \"\"quasilocal\"\" operators on the space of states of a given relativistic quantum theory. 1'/ This problem is specialized to the problem of constructing a model relativistic quantum theory of a certain type. The procedure used is to attempt to construct a representation of the generators of the Poincare group on the Fock space X of real scalarbosons in such a way that quasilocal observables are easily expressible in terms of the canonical creation-destruction operators. The structure of the model permits the construction of the generators to be approached by successively satisfying their structure relations in each of the spaces ~(n) specified by the eigenvalues of the free field particle number operator. These structure relations are satisfied in~(l) and~(2). The mathematical details of the problem increase rapidly with n, and no explicit solution is obtained for n > 2. Arguments are given which make it plausible that the structure relations in~(n), with n> 2, may be satisfied by a large class of generators. Several trial solutions in the space ~(3) are described, and the difficulties associated with them are discussed.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-31T15:21:22Z No. of bitstreams: 1 1966_nance.pdf: 2230808 bytes, checksum: 9b2bd845dc8e12b3d7bbb294e3840fbf (MD5)","Made available in DSpace on 2011-05-31T15:21:22Z (GMT). No. of bitstreams: 1 1966_nance.pdf: 2230808 bytes, checksum: 9b2bd845dc8e12b3d7bbb294e3840fbf (MD5) Previous issue date: 1966","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-31T15:21:22Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:11:24-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Thesis","U of I Only"],"dc:identifier":["6128057","http://hdl.handle.net/2142/25062"],"dc:language":["en"],"dc:rights":["1966 Jon Roland Nance"],"dc:subject":["macroscopically local relativistic quantum theory","relativistic quantum theory","field theory","scattering theory","quasilocal observables","scalar boson model"],"dc:title":["On the construction of macroscopically local relativistic quantum theories"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:24Z"}