{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23967"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23967","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"An integral equation for the anomalous deuteron vertex and a comparison of two normalization conditions","abstract":"\"A set of coupled inhomogeneous integral equations is found for the imaginary parts of the four invariant amplitudes of the anomalous deuteron vertex. The equations are algebraically homogeneous~ however, so the possibility of an eigenvalue con= \\ dition exists if unsubtracted dispersion relations are postulatedo The anomalous region is treated by means of a modification of the Nishijima continuation procedure. The equations are derived in a one pion model to illustrate the method. A partial diagrammatic analysis of the deuteron vertex is performed below the normal threshold o So = {M+~)2o In the second part a proof is given that the propagator normalization of a scalar or a vector particle is equivalent to the normalization of its electromagnetic form fqctoro The basis for the proof is the Ward identityo This permits a direct comparison of the two normalization conditions and this is done in lowest approximation for two scalar deuteron models and for the vector case as welL The normalization of the deuteron vertex is computed from the triangl,e·graph apprbximation to the deuteron ·electromagnet:i.c form factor. , I . This result is. inserted into the eXJ?ansion arising from the· dispersion relatio~ for' the inverse deuteron propagator at infinity, and an approximation to the deuteron field operator renormalization constant Z is thereby found. The result in each of the scalar models is Z = O. The vector case is more , sensitive to the form factors which enter 'in, but in a model which is in spirit comparable to the scalar examples yields Z =: o. An independent argument for Z = 0 for a vector field is advanced when no zero\"\":mass scalar particles are present.\"","abstract_html":""A set of coupled inhomogeneous integral equations is found for the imaginary parts of the four invariant amplitudes of the anomalous deuteron vertex. The equations are algebraically homogeneous~ however, so the possibility of an eigenvalue con= \\ dition exists if unsubtracted dispersion relations are postulatedo The anomalous region is treated by means of a modification of the Nishijima continuation procedure. The equations are derived in a one pion model to illustrate the method. A partial diagrammatic analysis of the deuteron vertex is performed below the normal threshold o So = {M+~)2o In the second part a proof is given that the propagator normalization of a scalar or a vector particle is equivalent to the normalization of its electromagnetic form fqctoro The basis for the proof is the Ward identityo This permits a direct comparison of the two normalization conditions and this is done in lowest approximation for two scalar deuteron models and for the vector case as welL The normalization of the deuteron vertex is computed from the triangl,e·graph apprbximation to the deuteron ·electromagnet:i.c form factor. , I . This result is. inserted into the eXJ?ansion arising from the· dispersion relatio~ for' the inverse deuteron propagator at infinity, and an approximation to the deuteron field operator renormalization constant Z is thereby found. The result in each of the scalar models is Z = O. The vector case is more , sensitive to the form factors which enter 'in, but in a model which is in spirit comparable to the scalar examples yields Z =: o. An independent argument for Z = 0 for a vector field is advanced when no zero"":mass scalar particles are present."","abstract_has_math":false,"creators":["Cawley, Robert Gerald"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Nishijima, K."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-19T15:59:55Z","date_published":"2011-05-19T15:59:55Z","updated_at":"2026-07-22T22:25:23Z","subjects":["coupled inhomogeneous integral equations","anomalous deutron vertex","normalization conditions","eigenvalue condition","Nishijima continuation"],"languages":["en"],"rights":["1965 Robert Gerald Cawley"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["6199209"],"render_values":[{"text":"6199209","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23967","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Nishijima, K."]},{"key":"dc:creator","label":"Author","values":["Cawley, Robert Gerald"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-19T15:59:55Z","10000-01-01","1965"]},{"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":["coupled inhomogeneous integral equations","anomalous deutron vertex","normalization conditions","eigenvalue condition","Nishijima continuation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["1965 Robert Gerald Cawley"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["6199209","http://hdl.handle.net/2142/23967"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"A set of coupled inhomogeneous integral equations is found for the imaginary parts of the four invariant amplitudes of the anomalous deuteron vertex. The equations are algebraically homogeneous~ however, so the possibility of an eigenvalue con= \\ dition exists if unsubtracted dispersion relations are postulatedo The anomalous region is treated by means of a modification of the Nishijima continuation procedure. The equations are derived in a one pion model to illustrate the method. A partial diagrammatic analysis of the deuteron vertex is performed below the normal threshold o So = {M+~)2o In the second part a proof is given that the propagator normalization of a scalar or a vector particle is equivalent to the normalization of its electromagnetic form fqctoro The basis for the proof is the Ward identityo This permits a direct comparison of the two normalization conditions and this is done in lowest approximation for two scalar deuteron models and for the vector case as welL The normalization of the deuteron vertex is computed from the triangl,e·graph apprbximation to the deuteron ·electromagnet:i.c form factor. , I . This result is. inserted into the eXJ?ansion arising from the· dispersion relatio~ for' the inverse deuteron propagator at infinity, and an approximation to the deuteron field operator renormalization constant Z is thereby found. The result in each of the scalar models is Z = O. The vector case is more , sensitive to the form factors which enter 'in, but in a model which is in spirit comparable to the scalar examples yields Z =: o. An independent argument for Z = 0 for a vector field is advanced when no zero\"\":mass scalar particles are present.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-19T15:59:55Z No. of bitstreams: 1 1965_cawley.pdf: 4954856 bytes, checksum: 1da8bfe193ef1598e4195ca92fba41c8 (MD5)","Made available in DSpace on 2011-05-19T15:59:55Z (GMT). No. of bitstreams: 1 1965_cawley.pdf: 4954856 bytes, checksum: 1da8bfe193ef1598e4195ca92fba41c8 (MD5) Previous issue date: 1965","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-19T15:59:55Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:14:01-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["An integral equation for the anomalous deuteron vertex and a comparison of two normalization conditions"]}]}],"canonical_facts":{"dc:contributor":["Nishijima, K."],"dc:creator":["Cawley, Robert Gerald"],"dc:date":["2011-05-19T15:59:55Z","10000-01-01","1965"],"dc:description":["\"A set of coupled inhomogeneous integral equations is found for the imaginary parts of the four invariant amplitudes of the anomalous deuteron vertex. The equations are algebraically homogeneous~ however, so the possibility of an eigenvalue con= \\ dition exists if unsubtracted dispersion relations are postulatedo The anomalous region is treated by means of a modification of the Nishijima continuation procedure. The equations are derived in a one pion model to illustrate the method. A partial diagrammatic analysis of the deuteron vertex is performed below the normal threshold o So = {M+~)2o In the second part a proof is given that the propagator normalization of a scalar or a vector particle is equivalent to the normalization of its electromagnetic form fqctoro The basis for the proof is the Ward identityo This permits a direct comparison of the two normalization conditions and this is done in lowest approximation for two scalar deuteron models and for the vector case as welL The normalization of the deuteron vertex is computed from the triangl,e·graph apprbximation to the deuteron ·electromagnet:i.c form factor. , I . This result is. inserted into the eXJ?ansion arising from the· dispersion relatio~ for' the inverse deuteron propagator at infinity, and an approximation to the deuteron field operator renormalization constant Z is thereby found. The result in each of the scalar models is Z = O. The vector case is more , sensitive to the form factors which enter 'in, but in a model which is in spirit comparable to the scalar examples yields Z =: o. An independent argument for Z = 0 for a vector field is advanced when no zero\"\":mass scalar particles are present.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-19T15:59:55Z No. of bitstreams: 1 1965_cawley.pdf: 4954856 bytes, checksum: 1da8bfe193ef1598e4195ca92fba41c8 (MD5)","Made available in DSpace on 2011-05-19T15:59:55Z (GMT). No. of bitstreams: 1 1965_cawley.pdf: 4954856 bytes, checksum: 1da8bfe193ef1598e4195ca92fba41c8 (MD5) Previous issue date: 1965","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-19T15:59:55Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:14:01-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Thesis","U of I Only"],"dc:identifier":["6199209","http://hdl.handle.net/2142/23967"],"dc:language":["en"],"dc:rights":["1965 Robert Gerald Cawley"],"dc:subject":["coupled inhomogeneous integral equations","anomalous deutron vertex","normalization conditions","eigenvalue condition","Nishijima continuation"],"dc:title":["An integral equation for the anomalous deuteron vertex and a comparison of two normalization conditions"],"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"}