{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/25706"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/25706","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Normalization of Bethe-Saltpeter amplitudes","abstract":"Two new derivations of the normalization condition for Bethe-Salpeter (bound state) amplitudes are presented. The first derivation is based on charge conservation. The normalization condition obtained is independent of the total charge of the system and, in principle, could be applied to a neutral system if we could regard a neutral system as being the limiting case of a charged one. The second derivation is based on energy-momentum conservation. The final result is precisely of the same form as the one obtained from charge conservation. We believe this to be the first derivation based on the expectation value of a conserved quantity which is applicable to all possible two-body systems, including neutral ones. Our results agree completely with the recent work of other authors who have used methods different from ours. Normalization of Wick's solution is presented as an illustration of the application of our normalization condition.","abstract_html":"Two new derivations of the normalization condition for Bethe-Salpeter (bound state) amplitudes are presented. The first derivation is based on charge conservation. The normalization condition obtained is independent of the total charge of the system and, in principle, could be applied to a neutral system if we could regard a neutral system as being the limiting case of a charged one. The second derivation is based on energy-momentum conservation. The final result is precisely of the same form as the one obtained from charge conservation. We believe this to be the first derivation based on the expectation value of a conserved quantity which is applicable to all possible two-body systems, including neutral ones. Our results agree completely with the recent work of other authors who have used methods different from ours. Normalization of Wick's solution is presented as an illustration of the application of our normalization condition.","abstract_has_math":false,"creators":["Singh, Amarjit Harnamsingh"],"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":"2011-07-07T20:25:54Z","date_published":"2011-07-07T20:25:54Z","updated_at":"2026-07-22T22:25:26Z","subjects":["normalization condition","Bethe-Salpeter amplitudes","neutral system","energy-momentum conservation"],"languages":["en"],"rights":["1967 Amarjit Harnamsingh Singh"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["6087275"],"render_values":[{"text":"6087275","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/25706","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":["Singh, Amarjit Harnamsingh"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-07-07T20:25:54Z","10000-01-01","1967"]},{"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":["normalization condition","Bethe-Salpeter amplitudes","neutral system","energy-momentum conservation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["1967 Amarjit Harnamsingh Singh"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["6087275","http://hdl.handle.net/2142/25706"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Two new derivations of the normalization condition for Bethe-Salpeter (bound state) amplitudes are presented. The first derivation is based on charge conservation. The normalization condition obtained is independent of the total charge of the system and, in principle, could be applied to a neutral system if we could regard a neutral system as being the limiting case of a charged one. The second derivation is based on energy-momentum conservation. The final result is precisely of the same form as the one obtained from charge conservation. We believe this to be the first derivation based on the expectation value of a conserved quantity which is applicable to all possible two-body systems, including neutral ones. Our results agree completely with the recent work of other authors who have used methods different from ours. Normalization of Wick's solution is presented as an illustration of the application of our normalization condition.","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-07-07T20:25:54Z No. of bitstreams: 1 1967_singh.pdf: 1945088 bytes, checksum: 1b3f34539195e7df1763f9276ffa299e (MD5)","Made available in DSpace on 2011-07-07T20:25:54Z (GMT). No. of bitstreams: 1 1967_singh.pdf: 1945088 bytes, checksum: 1b3f34539195e7df1763f9276ffa299e (MD5) Previous issue date: 1967","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-07-07T20:25:54Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:32:49-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["Normalization of Bethe-Saltpeter amplitudes"]}]}],"canonical_facts":{"dc:contributor":["Nishijima, K."],"dc:creator":["Singh, Amarjit Harnamsingh"],"dc:date":["2011-07-07T20:25:54Z","10000-01-01","1967"],"dc:description":["Two new derivations of the normalization condition for Bethe-Salpeter (bound state) amplitudes are presented. The first derivation is based on charge conservation. The normalization condition obtained is independent of the total charge of the system and, in principle, could be applied to a neutral system if we could regard a neutral system as being the limiting case of a charged one. The second derivation is based on energy-momentum conservation. The final result is precisely of the same form as the one obtained from charge conservation. We believe this to be the first derivation based on the expectation value of a conserved quantity which is applicable to all possible two-body systems, including neutral ones. Our results agree completely with the recent work of other authors who have used methods different from ours. Normalization of Wick's solution is presented as an illustration of the application of our normalization condition.","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-07-07T20:25:54Z No. of bitstreams: 1 1967_singh.pdf: 1945088 bytes, checksum: 1b3f34539195e7df1763f9276ffa299e (MD5)","Made available in DSpace on 2011-07-07T20:25:54Z (GMT). No. of bitstreams: 1 1967_singh.pdf: 1945088 bytes, checksum: 1b3f34539195e7df1763f9276ffa299e (MD5) Previous issue date: 1967","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-07-07T20:25:54Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:32:49-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Thesis","U of I Only"],"dc:identifier":["6087275","http://hdl.handle.net/2142/25706"],"dc:language":["en"],"dc:rights":["1967 Amarjit Harnamsingh Singh"],"dc:subject":["normalization condition","Bethe-Salpeter amplitudes","neutral system","energy-momentum conservation"],"dc:title":["Normalization of Bethe-Saltpeter amplitudes"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:26Z"}